modifications et création de la copie pour le dépôt final avec les règles de la FESP
This commit is contained in:
François Pelletier
parent
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commit
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89 changed files with 13756 additions and 1962 deletions
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memoire/.Rhistory
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memoire/.Rhistory
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\gdef\HyperFirstAtBeginDocument#1{#1}
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\providecommand\HyField@AuxAddToFields[1]{}
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\providecommand\HyField@AuxAddToCoFields[2]{}
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\bibstyle{plainnatmod}
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\bibstyle{plainnat-fr}
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\select@language{french}
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\@writefile{toc}{\select@language{french}}
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\@writefile{lof}{\select@language{french}}
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@ -62,8 +62,8 @@
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\bibcite{black1973pricing}{{7}{1973}{{Black et Scholes}}{{}}}
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\bibcite{buckle1995bayesian}{{8}{1995}{{Buckle}}{{}}}
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\bibcite{butler2007saddlepoint}{{9}{2007}{{Butler}}{{}}}
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\bibcite{carr1999option}{{10}{1999}{{Carr et Madan}}{{}}}
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\bibcite{madan1998variance}{{11}{1998}{{Carr et~al.}}{{Carr, Chang, et Madan}}}
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\bibcite{madan1998variance}{{10}{1998}{{Carr \emph {et~al.}}}{{Carr, Chang, et Madan}}}
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\bibcite{carr1999option}{{11}{1999}{{Carr et Madan}}{{}}}
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\bibcite{crowder1986consistency}{{12}{1986}{{Crowder}}{{}}}
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\bibcite{crowder1987linear}{{13}{1987}{{Crowder}}{{}}}
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\@writefile{toc}{\contentsline {chapter}{Bibliographie}{131}{section*.62}}
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@ -87,7 +87,7 @@
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\bibcite{hogg1978introduction}{{31}{1978}{{Hogg et Craig}}{{}}}
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\bibcite{itkin2005pricing}{{32}{2005}{{Itkin}}{{}}}
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\bibcite{wang2003evaluating}{{33}{2003}{{{Jingbo Wang} et Marsaglia}}{{}}}
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\bibcite{kotz2001laplace}{{34}{2001}{{Kotz et~al.}}{{Kotz, Kozubowski, et Podg{\'o}rski}}}
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\bibcite{kotz2001laplace}{{34}{2001}{{Kotz \emph {et~al.}}}{{Kotz, Kozubowski, et Podg{\'o}rski}}}
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\bibcite{KOUTROUVELIS01011980}{{35}{1980}{{Koutrouvelis}}{{}}}
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\bibcite{kozubowski1999class}{{36}{1999}{{Kozubowski et Podg{\'o}rski}}{{}}}
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\bibcite{kozubowski2001asymmetric}{{37}{2001}{{Kozubowski et Podg{\'o}rski}}{{}}}
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@ -98,7 +98,7 @@
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\bibcite{madan1990variance}{{42}{1990}{{Madan et Seneta}}{{}}}
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\bibcite{mandelbrot1963variation}{{43}{1963}{{Mandelbrot}}{{}}}
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\bibcite{merton1976option}{{44}{1976}{{Merton}}{{}}}
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\bibcite{barndorff2001levy}{{45}{2001}{{Mikosch et~al.}}{{Mikosch, Resnick, et Barndorff-Nielsen}}}
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\bibcite{barndorff2001levy}{{45}{2001}{{Mikosch \emph {et~al.}}}{{Mikosch, Resnick, et Barndorff-Nielsen}}}
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\bibcite{mitchell1916critique}{{46}{1916}{{Mitchell}}{{}}}
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\bibcite{newey1994large}{{47}{1994}{{Newey et McFadden}}{{}}}
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\bibcite{newey1987hypothesis}{{48}{1987}{{Newey et West}}{{}}}
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memoire/908144032.bbl
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memoire/908144032.bbl
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\begin{thebibliography}{63}
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\expandafter\ifx\csname natexlab\endcsname\relax\def\natexlab#1{#1}\fi
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\expandafter\ifx\csname fonteauteurs\endcsname\relax
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\def\fonteauteurs{\scshape}\fi
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\expandafter\ifx\csname url\endcsname\relax
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\def\url#1{{\tt #1}}%
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\message{You should include the url package}\fi
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||||
\bibitem[Abramowitz et Stegun(1965)]{abramowitz1965handbook}
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||||
Milton \bgroup\fonteauteurs\bgroup Abramowitz\egroup\egroup{} et Irene~A.
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||||
\bgroup\fonteauteurs\bgroup Stegun\egroup\egroup{} :
|
||||
\newblock {\em {H}andbook of {M}athematical {F}unctions: with {F}ormulas,
|
||||
{G}raphs, and {M}athematical {T}ables}, volume~55.
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||||
\newblock Dover Publications, 1965.
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||||
|
||||
\bibitem[Applebaum(2004)]{applebaum2004levy}
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||||
David \bgroup\fonteauteurs\bgroup Applebaum\egroup\egroup{} :
|
||||
\newblock {L}{\'e}vy {P}rocesses: {F}rom {P}robability to {F}inance and
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||||
{Q}uantum {G}roups.
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||||
\newblock {\em Notices of the American Mathematical Society}, 51\penalty0
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(11)\string:\penalty500\relax 1336--1347, 2004.
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||||
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||||
\bibitem[Bachelier(1900)]{bachelier1900theorie}
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Louis \bgroup\fonteauteurs\bgroup Bachelier\egroup\egroup{} :
|
||||
\newblock {\em {T}h{\'e}orie de la sp{\'e}culation}.
|
||||
\newblock Gauthier-Villars, 1900.
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||||
|
||||
\bibitem[Berkson(1980)]{berkson1980minimum}
|
||||
Joseph \bgroup\fonteauteurs\bgroup Berkson\egroup\egroup{} :
|
||||
\newblock {M}inimum {C}hi-square, not {M}aximum {L}ikelihood!
|
||||
\newblock {\em The Annals of Statistics}, pages 457--487, 1980.
|
||||
|
||||
\bibitem[Bingham et Kiesel(2004)]{bingham2004risk}
|
||||
Nicholas~H. \bgroup\fonteauteurs\bgroup Bingham\egroup\egroup{} et R{\"u}diger
|
||||
\bgroup\fonteauteurs\bgroup Kiesel\egroup\egroup{} :
|
||||
\newblock {\em {R}isk-Neutral {V}aluation: {P}ricing and {H}edging of
|
||||
{F}inancial {D}erivatives}.
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||||
\newblock Springer, 2004.
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||||
|
||||
\bibitem[Black(1976)]{black1976pricing}
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||||
Fischer \bgroup\fonteauteurs\bgroup Black\egroup\egroup{} :
|
||||
\newblock {T}he {P}ricing of {C}ommodity {C}ontracts.
|
||||
\newblock {\em Journal of Financial Economics}, 3\penalty0
|
||||
(1)\string:\penalty500\relax 167--179, 1976.
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||||
|
||||
\bibitem[Black et Scholes(1973)]{black1973pricing}
|
||||
Fischer \bgroup\fonteauteurs\bgroup Black\egroup\egroup{} et Myron
|
||||
\bgroup\fonteauteurs\bgroup Scholes\egroup\egroup{} :
|
||||
\newblock {T}he {P}ricing of {O}ptions and {C}orporate {L}iabilities.
|
||||
\newblock {\em The Journal of Political Economy}, pages 637--654, 1973.
|
||||
|
||||
\bibitem[Buckle(1995)]{buckle1995bayesian}
|
||||
D.~J. \bgroup\fonteauteurs\bgroup Buckle\egroup\egroup{} :
|
||||
\newblock {B}ayesian {I}nference for {S}table {D}istributions.
|
||||
\newblock {\em Journal of the American Statistical Association}, 90\penalty0
|
||||
(430)\string:\penalty500\relax 605--613, 1995.
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||||
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||||
\bibitem[Butler(2007)]{butler2007saddlepoint}
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||||
Ronald~W. \bgroup\fonteauteurs\bgroup Butler\egroup\egroup{} :
|
||||
\newblock {\em {S}addlepoint {A}pproximations with {A}pplications}, volume~22.
|
||||
\newblock Cambridge University Press, 2007.
|
||||
|
||||
\bibitem[Carr \emph{et~al.}(1998)Carr, Chang, et Madan]{madan1998variance}
|
||||
Peter~P. \bgroup\fonteauteurs\bgroup Carr\egroup\egroup{}, Eric~C.
|
||||
\bgroup\fonteauteurs\bgroup Chang\egroup\egroup{} et Dilip~B.
|
||||
\bgroup\fonteauteurs\bgroup Madan\egroup\egroup{} :
|
||||
\newblock {T}he {V}ariance {G}amma {P}rocess and {O}ption {P}ricing.
|
||||
\newblock {\em European Finance Review}, 2\penalty0
|
||||
(1)\string:\penalty500\relax 79--105, 1998.
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||||
|
||||
\bibitem[Carr et Madan(1999)]{carr1999option}
|
||||
Peter~P. \bgroup\fonteauteurs\bgroup Carr\egroup\egroup{} et Dilip~B.
|
||||
\bgroup\fonteauteurs\bgroup Madan\egroup\egroup{} :
|
||||
\newblock {O}ption {V}aluation {U}sing the {F}ast {F}ourier {T}ransform.
|
||||
\newblock {\em Journal of Computational Finance}, 2\penalty0
|
||||
(4)\string:\penalty500\relax 61--73, 1999.
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||||
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||||
\bibitem[Crowder(1986)]{crowder1986consistency}
|
||||
Martin \bgroup\fonteauteurs\bgroup Crowder\egroup\egroup{} :
|
||||
\newblock {O}n {C}onsistency and {I}nconsistency of {E}stimating {E}quations.
|
||||
\newblock {\em Econometric Theory}, pages 305--330, 1986.
|
||||
|
||||
\bibitem[Crowder(1987)]{crowder1987linear}
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||||
Martin \bgroup\fonteauteurs\bgroup Crowder\egroup\egroup{} :
|
||||
\newblock {O}n {L}inear and {Q}uadratic {E}stimating {F}unctions.
|
||||
\newblock {\em Biometrika}, 74\penalty0 (3)\string:\penalty500\relax 591--597,
|
||||
1987.
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||||
|
||||
\bibitem[Daniels(1954)]{daniels1954saddlepoint}
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||||
Henry~E. \bgroup\fonteauteurs\bgroup Daniels\egroup\egroup{} :
|
||||
\newblock {S}addlepoint {A}pproximations in {S}tatistics.
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||||
\newblock {\em The Annals of Mathematical Statistics}, pages 631--650, 1954.
|
||||
|
||||
\bibitem[Derman(1996)]{derman1996modelrisk}
|
||||
Emanuel \bgroup\fonteauteurs\bgroup Derman\egroup\egroup{} :
|
||||
\newblock {M}odel {R}isk.
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||||
\newblock Rapport technique, Goldman Sachs, 1996.
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||||
|
||||
\bibitem[Dodge(2004)]{dodge2004statistique}
|
||||
Yadolah \bgroup\fonteauteurs\bgroup Dodge\egroup\egroup{} :
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||||
\newblock {\em {S}tatistique: {D}ictionnaire Encyclop{\'e}dique}.
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||||
\newblock Springer Verlag France, 2004.
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||||
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||||
\bibitem[Epps(2007)]{epps2007pricing}
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||||
Thomas~W. \bgroup\fonteauteurs\bgroup Epps\egroup\egroup{} :
|
||||
\newblock {\em {P}ricing {D}erivative {S}ecurities}.
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||||
\newblock World Scientific Publishing Company incorporated, 2007.
|
||||
|
||||
\bibitem[Epps et Pulley(1983)]{epps1983test}
|
||||
Thomas~W. \bgroup\fonteauteurs\bgroup Epps\egroup\egroup{} et Lawrence~B.
|
||||
\bgroup\fonteauteurs\bgroup Pulley\egroup\egroup{} :
|
||||
\newblock {A} {T}est for {N}ormality {B}ased on the {E}mpirical
|
||||
{C}haracteristic {F}unction.
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||||
\newblock {\em Biometrika}, 70\penalty0 (3)\string:\penalty500\relax 723--726,
|
||||
1983.
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||||
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||||
\bibitem[Everitt et Skrondal(2006)]{everitt2006cambridge}
|
||||
Brian \bgroup\fonteauteurs\bgroup Everitt\egroup\egroup{} et Anders
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||||
\bgroup\fonteauteurs\bgroup Skrondal\egroup\egroup{} :
|
||||
\newblock {\em {T}he {C}ambridge {D}ictionary of {S}tatistics}, volume~4.
|
||||
\newblock Cambridge University Press, 2006.
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||||
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||||
\bibitem[Fama et French(1993)]{fama1993common}
|
||||
Eugene~F. \bgroup\fonteauteurs\bgroup Fama\egroup\egroup{} et Kenneth~R.
|
||||
\bgroup\fonteauteurs\bgroup French\egroup\egroup{} :
|
||||
\newblock {C}ommon {R}isk {F}actors in the {R}eturns on {S}tocks and {B}onds.
|
||||
\newblock {\em Journal of Financial Economics}, 33\penalty0
|
||||
(1)\string:\penalty500\relax 3--56, 1993.
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||||
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||||
\bibitem[Feuerverger et McDunnough(1981)]{feuerverger1981efficiency}
|
||||
Andrey \bgroup\fonteauteurs\bgroup Feuerverger\egroup\egroup{} et Philip
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||||
\bgroup\fonteauteurs\bgroup McDunnough\egroup\egroup{} :
|
||||
\newblock {O}n the {E}fficiency of {E}mpirical {C}haracteristic {F}unction
|
||||
{P}rocedures.
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||||
\newblock {\em Journal of the Royal Statistical Society. Series B
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||||
(methodological)}, pages 20--27, 1981.
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||||
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||||
\bibitem[Fox et Taqqu(1986)]{fox1986large}
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||||
Robert \bgroup\fonteauteurs\bgroup Fox\egroup\egroup{} et Murad~S.
|
||||
\bgroup\fonteauteurs\bgroup Taqqu\egroup\egroup{} :
|
||||
\newblock {L}arge-sample {P}roperties of {P}arameter {E}stimates for {S}trongly
|
||||
{D}ependent {S}tationary {G}aussian {T}ime {S}eries.
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||||
\newblock {\em The Annals of Statistics}, 14\penalty0
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||||
(2)\string:\penalty500\relax 517--532, 1986.
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||||
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||||
\bibitem[Gil-Pelaez(1951)]{gil1951note}
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||||
J.~\bgroup\fonteauteurs\bgroup Gil-Pelaez\egroup\egroup{} :
|
||||
\newblock {N}ote on the {I}nversion {T}heorem.
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\newblock {\em Biometrika}, 38\penalty0 (3-4)\string:\penalty500\relax
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||||
481--482, 1951.
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||||
\bibitem[Gourieroux et Monfort(1989)]{gourieroux1989statistique}
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||||
Christian \bgroup\fonteauteurs\bgroup Gourieroux\egroup\egroup{} et Alain
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\bgroup\fonteauteurs\bgroup Monfort\egroup\egroup{} :
|
||||
\newblock {\em {S}tatistique et Mod{\`e}les {\'E}conom{\'e}triques: Notions
|
||||
G{\'e}n{\'e}rales, Estimation, Pr{\'e}vision, Algorithmes}, volume~1.
|
||||
\newblock Economica, 1989.
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||||
|
||||
\bibitem[Hall(2005)]{hall2005generalized}
|
||||
Alastair~R. \bgroup\fonteauteurs\bgroup Hall\egroup\egroup{} :
|
||||
\newblock {\em {G}eneralized {M}ethod of {M}oments}.
|
||||
\newblock Oxford University Press, 2005.
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||||
|
||||
\bibitem[Hamilton(1994)]{hamilton1994time}
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||||
James~Douglas \bgroup\fonteauteurs\bgroup Hamilton\egroup\egroup{} :
|
||||
\newblock {\em {T}ime {S}eries {A}nalysis}, volume~2.
|
||||
\newblock Cambridge University Press, 1994.
|
||||
|
||||
\bibitem[Hansen(1982)]{hansen1982large}
|
||||
Lars~Peter \bgroup\fonteauteurs\bgroup Hansen\egroup\egroup{} :
|
||||
\newblock {L}arge {S}ample {P}roperties of {G}eneralized {M}ethod of {M}oments
|
||||
{E}stimators.
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||||
\newblock {\em Econometrica}, pages 1029--1054, 1982.
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||||
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||||
\bibitem[Henze(1990)]{henze1990approximation}
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||||
Norbert \bgroup\fonteauteurs\bgroup Henze\egroup\egroup{} :
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||||
\newblock {A}n {A}pproximation to the {L}imit {D}istribution of the
|
||||
{E}pps-{P}ulley {T}est {S}tatistic for {N}ormality.
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||||
\newblock {\em Metrika}, 37\penalty0 (1)\string:\penalty500\relax 7--18, 1990.
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||||
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||||
\bibitem[Heston(1993)]{heston1993closed}
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||||
Steven~L. \bgroup\fonteauteurs\bgroup Heston\egroup\egroup{} :
|
||||
\newblock {A} {C}losed-{F}orm {S}olution for {O}ptions with {S}tochastic
|
||||
{V}olatility with {A}pplications to {B}ond and {C}urrency {O}ptions.
|
||||
\newblock {\em Review of Financial Studies}, 6\penalty0
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||||
(2)\string:\penalty500\relax 327--343, 1993.
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||||
|
||||
\bibitem[Hinkley et Revankar(1977)]{hinkley1977estimation}
|
||||
David~V. \bgroup\fonteauteurs\bgroup Hinkley\egroup\egroup{} et Nagesh~S.
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||||
\bgroup\fonteauteurs\bgroup Revankar\egroup\egroup{} :
|
||||
\newblock {E}stimation of the {P}areto {L}aw from {U}nderreported {D}ata: {A}
|
||||
{F}urther {A}nalysis.
|
||||
\newblock {\em Journal of Econometrics}, 5\penalty0
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||||
(1)\string:\penalty500\relax 1--11, 1977.
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||||
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||||
\bibitem[Hogg et Craig(1978)]{hogg1978introduction}
|
||||
Robert~V. \bgroup\fonteauteurs\bgroup Hogg\egroup\egroup{} et Allen
|
||||
\bgroup\fonteauteurs\bgroup Craig\egroup\egroup{} :
|
||||
\newblock {\em {I}ntroduction to {M}athematical {S}tatistics}.
|
||||
\newblock Macmillan, 1978.
|
||||
|
||||
\bibitem[Itkin(2005)]{itkin2005pricing}
|
||||
Andrey \bgroup\fonteauteurs\bgroup Itkin\egroup\egroup{} :
|
||||
\newblock {P}ricing {O}ptions with {VG} {M}odel {U}sing {FFT}.
|
||||
\newblock {\em arXiv preprint physics/0503137}, 2005.
|
||||
|
||||
\bibitem[{Jingbo Wang} et Marsaglia(2003)]{wang2003evaluating}
|
||||
Wai Wan~Tsang \bgroup\fonteauteurs\bgroup {Jingbo Wang}\egroup\egroup{} et
|
||||
George \bgroup\fonteauteurs\bgroup Marsaglia\egroup\egroup{} :
|
||||
\newblock {E}valuating {K}olmogorov's {D}istribution.
|
||||
\newblock {\em Journal of Statistical Software}, 8\penalty0
|
||||
(18)\string:\penalty500\relax 1--4, 2003.
|
||||
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||||
\bibitem[Kotz \emph{et~al.}(2001)Kotz, Kozubowski, et
|
||||
Podg{\'o}rski]{kotz2001laplace}
|
||||
Samuel \bgroup\fonteauteurs\bgroup Kotz\egroup\egroup{}, Tomasz~J.
|
||||
\bgroup\fonteauteurs\bgroup Kozubowski\egroup\egroup{} et Krzystof
|
||||
\bgroup\fonteauteurs\bgroup Podg{\'o}rski\egroup\egroup{} :
|
||||
\newblock {\em {T}he {L}aplace {D}istribution and {G}eneralizations: {A}
|
||||
{R}evisit with {A}pplications to {C}ommunications, {E}conomics,
|
||||
{E}ngineering, and {F}inance}.
|
||||
\newblock Progress in Mathematics Series. Birkh{\"a}user, 2001.
|
||||
|
||||
\bibitem[Koutrouvelis(1980)]{KOUTROUVELIS01011980}
|
||||
Ioannis~A. \bgroup\fonteauteurs\bgroup Koutrouvelis\egroup\egroup{} :
|
||||
\newblock {{A} {G}oodness-{O}f-{F}it {T}est of {S}imple {H}ypotheses {B}ased on
|
||||
the {E}mpirical {C}haracteristic {F}unction}.
|
||||
\newblock {\em {B}iometrika}, 67\penalty0 (1)\string:\penalty500\relax
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||||
238--240, 1980.
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||||
\bibitem[Kozubowski et Podg{\'o}rski(1999)]{kozubowski1999class}
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||||
Tomasz~J. \bgroup\fonteauteurs\bgroup Kozubowski\egroup\egroup{} et Krzysztof
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||||
\bgroup\fonteauteurs\bgroup Podg{\'o}rski\egroup\egroup{} :
|
||||
\newblock {A} {C}lass of {A}symmetric {D}istributions.
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||||
\newblock {\em Actuarial Research Clearing House}, 1\string:\penalty500\relax
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||||
113--134, 1999.
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\bibitem[Kozubowski et Podg{\'o}rski(2001)]{kozubowski2001asymmetric}
|
||||
Tomasz~J. \bgroup\fonteauteurs\bgroup Kozubowski\egroup\egroup{} et Krzysztof
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||||
\bgroup\fonteauteurs\bgroup Podg{\'o}rski\egroup\egroup{} :
|
||||
\newblock {A}symmetric {L}aplace {L}aws and {M}odeling {F}inancial {D}ata.
|
||||
\newblock {\em {M}athematical and {C}omputer {M}odeling}, 34\penalty0
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||||
(9)\string:\penalty500\relax 1003--1021, 2001.
|
||||
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||||
\bibitem[Kyprianou(2007)]{kyprianou2007introductory}
|
||||
Andreas~E. \bgroup\fonteauteurs\bgroup Kyprianou\egroup\egroup{} :
|
||||
\newblock {\em {I}ntroductory {L}ectures on {F}luctuations of {L}{\'e}vy
|
||||
{P}rocesses with {A}pplications}.
|
||||
\newblock Springer, 2007.
|
||||
|
||||
\bibitem[Lugannani et Rice(1980)]{lugannani1980saddle}
|
||||
Robert \bgroup\fonteauteurs\bgroup Lugannani\egroup\egroup{} et Stephen
|
||||
\bgroup\fonteauteurs\bgroup Rice\egroup\egroup{} :
|
||||
\newblock {S}addle {P}oint {A}pproximation for the {D}istribution of the {S}um
|
||||
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||||
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||||
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||||
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||||
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||||
\newblock {L}arge {S}ample {E}stimation and {H}ypothesis {T}esting.
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||||
\bgroup\fonteauteurs\bgroup West\egroup\egroup{} :
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||||
\newblock {H}ypothesis {T}esting with {E}fficient {M}ethod of {M}oments
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||||
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||||
\newblock {T}he {D}istribution of {S}hare {P}rice {C}hanges.
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||||
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||||
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||||
S.~James \bgroup\fonteauteurs\bgroup Press\egroup\egroup{} :
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||||
\newblock {A} {C}ompound {E}vents {M}odel for {S}ecurity {P}rices.
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||||
\newblock {\em Journal of Business}, pages 317--335, 1967.
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||||
|
||||
\bibitem[{Sato}(1999)]{sato1999levy}
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||||
{Ken-Iti} \bgroup\fonteauteurs\bgroup {Sato}\egroup\egroup{} :
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||||
\newblock {\em {L}{\'e}vy {P}rocesses and {I}nfinitely {D}ivisible
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||||
{D}istributions}.
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||||
\newblock Cambridge Studies in Advanced Mathematics. Cambridge University
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||||
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||||
|
||||
\bibitem[Schoutens(2003)]{schoutens2003levy}
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||||
Wim \bgroup\fonteauteurs\bgroup Schoutens\egroup\egroup{} :
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||||
\newblock {\em {L}{\'e}vy {P}rocesses in {F}inance}.
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||||
\newblock Wiley, 2003.
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||||
|
||||
\bibitem[Scott et Dong(2012)]{RpackageVarianceGamma}
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||||
David \bgroup\fonteauteurs\bgroup Scott\egroup\egroup{} et Christine~Yang
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||||
\bgroup\fonteauteurs\bgroup Dong\egroup\egroup{} :
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||||
\newblock {\em {{v}ariancegamma: {T}he {V}ariance {G}amma {D}istribution}},
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||||
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||||
\newblock URL \url{http://CRAN.R-project.org/package=VarianceGamma}.
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||||
\newblock Consulté le 24 janvier 2014.
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||||
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||||
\bibitem[Seneta(2004)]{seneta2004fitting}
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||||
Eugene \bgroup\fonteauteurs\bgroup Seneta\egroup\egroup{} :
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\newblock {F}itting the {V}ariance {G}amma {M}odel to {F}inancial {D}ata.
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||||
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||||
\bibitem[Shapiro et Wilk(1965)]{shapiro1965analysis}
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Samuel~Sanford \bgroup\fonteauteurs\bgroup Shapiro\egroup\egroup{} et Martin~B.
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||||
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||||
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||||
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||||
{T}ables}, volume 1000.
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||||
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||||
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\bibitem[Stuart et Ord(1987)]{stuart1987kendall}
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||||
\bgroup\fonteauteurs\bgroup Ord\egroup\egroup{} :
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||||
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||||
\newblock Oxford University Press, 1987.
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||||
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||||
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||||
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||||
\newblock URL \url{http://www.mat.univie.ac.at/~gerald/ftp/book-fa/index.html}.
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||||
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||||
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||||
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||||
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||||
of {M}arkets: {I}mplications for the {A}ctuaries and {E}mphasized
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||||
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||||
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||||
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||||
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||||
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||||
|
||||
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||||
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||||
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||||
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||||
Jeffrey~M. \bgroup\fonteauteurs\bgroup Wooldridge\egroup\egroup{} :
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||||
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||||
{D}ata}.
|
||||
\newblock MIT press, 2001.
|
||||
|
||||
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||||
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|
||||
\begin{figure}[!ht]
|
||||
\centering
|
||||
\includegraphics[scale=0.8]{"../graphiques/CH3-SIMULGAL0121"}
|
||||
\includegraphics[scale=0.8]{"./graphiques/CH3-SIMULGAL0121"}
|
||||
\caption{Histogramme et estimateur de densité par noyau de 2500
|
||||
réalisations de la variable aléatoire $Y\sim
|
||||
GAL(\theta=0,\sigma=1,\kappa=2,\tau=1)$}
|
||||
|
|
|
|||
|
|
@ -19,7 +19,7 @@ celui-ci a comme désavantage d'être très peu précis dans l'évaluation
|
|||
des probabilités aux extrémités du support de la densité (figure
|
||||
\ref{fig:probdroite}).
|
||||
\begin{figure}[!ht]
|
||||
\centering \input{../graphiques/probdroite.tex}
|
||||
\centering \input{./graphiques/probdroite.tex}
|
||||
\caption{Probabilité à l'extrémité du support}
|
||||
\label{fig:probdroite}
|
||||
\end{figure}
|
||||
|
|
@ -96,7 +96,7 @@ variable aléatoire $Z_{w_0}$ de distribution normale standard tronquée
|
|||
de telle sorte qu'elle ne puisse prendre des valeurs supérieures au
|
||||
point $w_0$.
|
||||
\begin{figure}[!ht]
|
||||
\centering \input{../graphiques/normaletronque.tex}
|
||||
\centering \input{./graphiques/normaletronque.tex}
|
||||
\caption{Distribution normale tronquée à $w_0$}
|
||||
\label{fig:normaletronque}
|
||||
\end{figure}
|
||||
|
|
|
|||
|
|
@ -18,7 +18,7 @@ la figure \ref{fig:seriechronoR1} sous forme de série chronologique.
|
|||
\begin{figure}[!ht]
|
||||
\centering
|
||||
\includegraphics[height=4in,
|
||||
width=4in]{../graphiques/ABBEYN-chronologie.pdf}
|
||||
width=4in]{./graphiques/ABBEYN-chronologie.pdf}
|
||||
\caption{Représentation en série chronologique de l'échantillon
|
||||
$R_1$}
|
||||
\label{fig:seriechronoR1}
|
||||
|
|
@ -69,7 +69,7 @@ d'une courbe de densité à la figure \ref{fig:distributionR1}.
|
|||
|
||||
\begin{figure}[!ht]
|
||||
\centering
|
||||
\includegraphics[height=4in,width=4in]{../graphiques/ABBEYN-histogramme.pdf}
|
||||
\includegraphics[height=4in,width=4in]{./graphiques/ABBEYN-histogramme.pdf}
|
||||
\caption{Distribution de la variable aléatoire $R_1$}
|
||||
\label{fig:distributionR1}
|
||||
\end{figure}
|
||||
|
|
@ -109,7 +109,7 @@ quantiles empiriques avec ceux de la loi normale présenté à la figure
|
|||
\begin{figure}[!ht]
|
||||
\centering
|
||||
\includegraphics[height=4in,
|
||||
width=4in]{../graphiques/ABBEYN-qq.pdf}
|
||||
width=4in]{./graphiques/ABBEYN-qq.pdf}
|
||||
\caption{Graphique Quantile-Quantile}
|
||||
\label{fig:qqplotR1}
|
||||
\end{figure}
|
||||
|
|
@ -395,7 +395,7 @@ On résout d'abord l'équation du point de selle
|
|||
$r=0.01$ à la figure \ref{fig:equationptselle0.01R1} :
|
||||
\begin{figure}[!ht]
|
||||
\centering
|
||||
\includegraphics[scale=0.5]{../graphiques/pointdeselleGMM.png}
|
||||
\includegraphics[scale=0.5]{./graphiques/pointdeselleGMM.png}
|
||||
\caption{Équation du point de selle pour $r=0.01$}
|
||||
\label{fig:equationptselle0.01R1}
|
||||
\end{figure}
|
||||
|
|
@ -513,7 +513,7 @@ la table \ref{tab:intapproxpointselleR1}.
|
|||
\begin{figure}[!ht]
|
||||
\centering
|
||||
\includegraphics[height=6in,
|
||||
width=6in]{../graphiques/ABBEYN-densiteGALmu-7.pdf}
|
||||
width=6in]{./graphiques/ABBEYN-densiteGALmu-7.pdf}
|
||||
\caption{Densité de $R_1^{*}$ selon la méthode des moments
|
||||
généralisée}
|
||||
\label{fig:densite1R1}
|
||||
|
|
@ -522,7 +522,7 @@ la table \ref{tab:intapproxpointselleR1}.
|
|||
\begin{figure}[!ht]
|
||||
\centering
|
||||
\includegraphics[height=6in,
|
||||
width=6in]{../graphiques/ABBEYN-densiteGALmu-5.pdf}
|
||||
width=6in]{./graphiques/ABBEYN-densiteGALmu-5.pdf}
|
||||
\caption{Densité de $R_1^{*}$ selon la méthode de l'équation
|
||||
d'estimation optimale}
|
||||
\label{fig:densite3R1}
|
||||
|
|
@ -681,7 +681,7 @@ d'ordre 1 est très précise dans ce contexte.
|
|||
\begin{figure}[!ht]
|
||||
\centering
|
||||
\includegraphics[height=6in,
|
||||
width=6in]{../graphiques/ABBEYN-callGAL-7.pdf}
|
||||
width=6in]{./graphiques/ABBEYN-callGAL-7.pdf}
|
||||
\caption{Prix de l'option selon les paramètres estimés avec la
|
||||
méthode des moments généralisée}
|
||||
\label{fig:prix1R1-1}
|
||||
|
|
@ -690,7 +690,7 @@ d'ordre 1 est très précise dans ce contexte.
|
|||
\begin{figure}[!ht]
|
||||
\centering
|
||||
\includegraphics[height=6in,
|
||||
width=6in]{../graphiques/ABBEYN-callGAL-5.pdf}
|
||||
width=6in]{./graphiques/ABBEYN-callGAL-5.pdf}
|
||||
\caption{Prix de l'option selon les paramètres estimés avec la
|
||||
méthode de l'équation d'estimation optimale}
|
||||
\label{fig:prix1R1-3}
|
||||
|
|
|
|||
|
|
@ -1,371 +0,0 @@
|
|||
\begin{thebibliography}{63}
|
||||
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|
||||
\providecommand{\url}[1]{\texttt{#1}}
|
||||
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|
||||
\providecommand{\doi}[1]{doi: #1}\else
|
||||
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|
||||
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||||
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{G}raphs, and {M}athematical {T}ables}, volume~55.
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||||
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|
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||||
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||||
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||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
|
||||
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|
||||
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|
||||
\newblock {M}inimum {C}hi-square, not {M}aximum {L}ikelihood!
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||||
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||||
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||||
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||||
|
||||
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||||
Fischer Black et Myron Scholes.
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||||
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||||
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|
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||||
\newblock {O}n {L}inear and {Q}uadratic {E}stimating {F}unctions.
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||||
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||||
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||||
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||||
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||||
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||||
|
||||
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Eugene~F. Fama et Kenneth~R. French.
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||||
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||||
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||||
{D}ependent {S}tationary {G}aussian {T}ime {S}eries.
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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|
||||
\newblock \emph{Journal of Business}, pages 511--524, 1990.
|
||||
|
||||
\bibitem[Mandelbrot(1963)]{mandelbrot1963variation}
|
||||
Benoit Mandelbrot.
|
||||
\newblock {T}he {V}ariation of {C}ertain {S}peculative {P}rices.
|
||||
\newblock \emph{Journal of Business}, pages 394--419, 1963.
|
||||
|
||||
\bibitem[Merton(1976)]{merton1976option}
|
||||
Robert~C. Merton.
|
||||
\newblock {O}ption {P}ricing when {U}nderlying {S}tock {R}eturns {A}re
|
||||
{D}iscontinuous.
|
||||
\newblock \emph{Journal of Financial Economics}, 3\penalty0 (1):\penalty0
|
||||
125--144, 1976.
|
||||
|
||||
\bibitem[Mikosch et~al.(2001)Mikosch, Resnick, et
|
||||
Barndorff-Nielsen]{barndorff2001levy}
|
||||
Thomas Mikosch, Sidney~I. Resnick, et Ole~E. Barndorff-Nielsen.
|
||||
\newblock \emph{{L}{\'e}vy {P}rocesses: {T}heory and {A}pplications}.
|
||||
\newblock Birkh{\"a}user, 2001.
|
||||
|
||||
\bibitem[Mitchell(1916)]{mitchell1916critique}
|
||||
Wesley~C. Mitchell.
|
||||
\newblock {A} {C}ritique of {I}ndex {N}umbers of the {P}rices of {S}tocks.
|
||||
\newblock \emph{The Journal of Political Economy}, pages 625--693, 1916.
|
||||
|
||||
\bibitem[Newey et McFadden(1994)]{newey1994large}
|
||||
Whitney~K. Newey et Daniel McFadden.
|
||||
\newblock {L}arge {S}ample {E}stimation and {H}ypothesis {T}esting.
|
||||
\newblock \emph{Handbook of Econometrics}, 4:\penalty0 2111--2245, 1994.
|
||||
|
||||
\bibitem[Newey et West(1987)]{newey1987hypothesis}
|
||||
Whitney~K. Newey et Kenneth~D. West.
|
||||
\newblock {H}ypothesis {T}esting with {E}fficient {M}ethod of {M}oments
|
||||
{E}stimation.
|
||||
\newblock \emph{International Economic Review}, 28\penalty0 (3):\penalty0
|
||||
777--787, 1987.
|
||||
|
||||
\bibitem[Praetz(1972)]{praetz1972distribution}
|
||||
Peter~D. Praetz.
|
||||
\newblock {T}he {D}istribution of {S}hare {P}rice {C}hanges.
|
||||
\newblock \emph{Journal of Business}, pages 49--55, 1972.
|
||||
|
||||
\bibitem[Press(1967)]{press1967compound}
|
||||
S.~James Press.
|
||||
\newblock {A} {C}ompound {E}vents {M}odel for {S}ecurity {P}rices.
|
||||
\newblock \emph{Journal of Business}, pages 317--335, 1967.
|
||||
|
||||
\bibitem[{Sato}(1999)]{sato1999levy}
|
||||
{Ken-Iti} {Sato}.
|
||||
\newblock \emph{{L}{\'e}vy {P}rocesses and {I}nfinitely {D}ivisible
|
||||
{D}istributions}.
|
||||
\newblock Cambridge Studies in Advanced Mathematics. Cambridge University
|
||||
Press, 1999.
|
||||
|
||||
\bibitem[Schoutens(2003)]{schoutens2003levy}
|
||||
Wim Schoutens.
|
||||
\newblock \emph{{L}{\'e}vy {P}rocesses in {F}inance}.
|
||||
\newblock Wiley, 2003.
|
||||
|
||||
\bibitem[Scott et Dong(2012)]{RpackageVarianceGamma}
|
||||
David Scott et Christine~Yang Dong.
|
||||
\newblock \emph{{{v}ariancegamma: {T}he {V}ariance {G}amma {D}istribution}},
|
||||
2012.
|
||||
\newblock URL \url{http://CRAN.R-project.org/package=VarianceGamma}.
|
||||
\newblock Consulté le 24 janvier 2014.
|
||||
|
||||
\bibitem[Seneta(2004)]{seneta2004fitting}
|
||||
Eugene Seneta.
|
||||
\newblock {F}itting the {V}ariance {G}amma {M}odel to {F}inancial {D}ata.
|
||||
\newblock \emph{Journal of Applied Probability}, pages 177--187, 2004.
|
||||
|
||||
\bibitem[Shapiro et Wilk(1965)]{shapiro1965analysis}
|
||||
Samuel~Sanford Shapiro et Martin~B. Wilk.
|
||||
\newblock {A}n {A}nalysis of {V}ariance {T}est for {N}ormality ({C}omplete
|
||||
{S}amples).
|
||||
\newblock \emph{Biometrika}, 52\penalty0 (3/4):\penalty0 591--611, 1965.
|
||||
|
||||
\bibitem[Shephard(1991)]{shephard1991characteristic}
|
||||
Neil~G. Shephard.
|
||||
\newblock {F}rom {C}haracteristic {F}unction to {D}istribution {F}unction: {A}
|
||||
{S}imple {F}ramework for the {T}heory.
|
||||
\newblock \emph{Econometric Theory}, 7\penalty0 (04):\penalty0 519--529, 1991.
|
||||
|
||||
\bibitem[Spiegel et Liu(1999)]{spiegel1999schaum}
|
||||
Murray~R. Spiegel et John Liu.
|
||||
\newblock \emph{{S}chaum's {M}athematical {H}andbook of {F}ormulas and
|
||||
{T}ables}, volume 1000.
|
||||
\newblock McGraw-Hill, 1999.
|
||||
|
||||
\bibitem[Stuart et Ord(1987)]{stuart1987kendall}
|
||||
Alan Stuart et J.~Keith Ord.
|
||||
\newblock \emph{{K}endall{\rq}s {A}dvanced {T}heory of {S}tatistics, {V}ol. 1}.
|
||||
\newblock Oxford University Press, 1987.
|
||||
|
||||
\bibitem[Teschl(2004)]{teschl2004topics}
|
||||
Gerald Teschl.
|
||||
\newblock \emph{{T}opics in {R}eal and {F}unctional {A}nalysis}, 2004.
|
||||
\newblock URL \url{http://www.mat.univie.ac.at/~gerald/ftp/book-fa/index.html}.
|
||||
\newblock Consulté le 24 janvier 2014.
|
||||
|
||||
\bibitem[Walter(1995)]{walterlevy}
|
||||
Christian Walter.
|
||||
\newblock {L}{\'e}vy-{S}tability {U}nder {A}ddition and {F}ractal {S}tructure
|
||||
of {M}arkets: {I}mplications for the {A}ctuaries and {E}mphasized
|
||||
{E}xamination of {MATIF} {N}ational {C}ontract.
|
||||
\newblock In \emph{Proceedings of the 5th AFIR colloquium}. International
|
||||
Actuarial Association, 1995.
|
||||
|
||||
\bibitem[Wendel(1961)]{wendel1961non}
|
||||
J.~G. Wendel.
|
||||
\newblock {T}he {N}on-{A}bsolute {C}onvergence of {G}il-{P}elaez' {I}nversion
|
||||
{I}ntegral.
|
||||
\newblock \emph{The Annals of Mathematical Statistics}, 32\penalty0
|
||||
(1):\penalty0 338--339, 1961.
|
||||
|
||||
\bibitem[Wolfowitz(1957)]{wolfowitz1957minimum}
|
||||
Jacob Wolfowitz.
|
||||
\newblock {T}he {M}inimum {D}istance {M}ethod.
|
||||
\newblock \emph{The Annals of Mathematical Statistics}, pages 75--88, 1957.
|
||||
|
||||
\bibitem[Wooldridge(2001)]{wooldridge2001econometric}
|
||||
Jeffrey~M. Wooldridge.
|
||||
\newblock \emph{{E}conometric {A}nalysis of {C}ross {S}ection and {P}anel
|
||||
{D}ata}.
|
||||
\newblock MIT press, 2001.
|
||||
|
||||
\end{thebibliography}
|
||||
BIN
memoire/graphiques/ABBEYN-callGAL-5.pdf
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memoire/graphiques/ABBEYN-callGAL-5.pdf
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memoire/graphiques/ABBEYN-callGAL-7.pdf
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memoire/graphiques/ABBEYN-callGAL-7.pdf
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memoire/graphiques/ABBEYN-chronologie.pdf
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memoire/graphiques/ABBEYN-chronologie.pdf
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memoire/graphiques/ABBEYN-densiteGALmu-5.pdf
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memoire/graphiques/ABBEYN-densiteGALmu-5.pdf
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memoire/graphiques/ABBEYN-densiteGALmu-7.pdf
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memoire/graphiques/ABBEYN-densiteGALmu-7.pdf
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memoire/graphiques/ABBEYN-histogramme.pdf
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memoire/graphiques/ABBEYN-histogramme.pdf
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memoire/graphiques/ABBEYN-qq.pdf
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memoire/graphiques/ABBEYN-qq.pdf
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1002
memoire/graphiques/CH3-SIMGAMMAGAUSS.csv
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1002
memoire/graphiques/CH3-SIMGAMMAGAUSS.csv
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File diff suppressed because it is too large
Load diff
BIN
memoire/graphiques/CH3-SIMGAMMAGAUSS.pdf
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BIN
memoire/graphiques/CH3-SIMGAMMAGAUSS.pdf
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memoire/graphiques/CH3-SIMULGAL0121.pdf
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memoire/graphiques/CH3-SIMULGAL0121.pdf
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24
memoire/graphiques/ch3.r
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24
memoire/graphiques/ch3.r
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|
|
@ -0,0 +1,24 @@
|
|||
set.seed(908144032)
|
||||
|
||||
## GRAPHIQUE 1 ##
|
||||
s0 <- 100
|
||||
n <- 500
|
||||
## On simule des temps d'arrivée Gamma
|
||||
t <- c(0,rep(cumsum(rgamma(n,0.5)),each=2))
|
||||
## On simule des sauts gaussiens
|
||||
j <- head(c(0,0,rep(cumsum(rnorm(n,0.005/365,0.0025)),each=2)),-1)
|
||||
## On trace le parcours
|
||||
cbind(t,j)
|
||||
pdf("CH3-SIMGAMMAGAUSS.pdf")
|
||||
plot(t,s0*exp(j),type="l",xlab="t",ylab="Y(t)",main=" ")
|
||||
dev.off()
|
||||
write.csv(data.frame(Temps=t,Prix=s0*exp(j)),file="CH3-SIMGAMMAGAUSS.csv")
|
||||
|
||||
## GRAPHIQUE 2 ##
|
||||
source("../contenus/r/code/rGAL.r")
|
||||
|
||||
d1 <- rGALkappa(2500,0,1,2,1)
|
||||
pdf("CH3-SIMULGAL0121.pdf")
|
||||
hist(d1,prob=TRUE,col="grey",breaks=25,xlab="y",ylab="f(y)",main="")
|
||||
lines(density(d1),lwd=3)
|
||||
dev.off()
|
||||
BIN
memoire/graphiques/dGAL-exemples.pdf
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memoire/graphiques/dGAL-exemples.pdf
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25
memoire/graphiques/dgal-exemples.r
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25
memoire/graphiques/dgal-exemples.r
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|
|
@ -0,0 +1,25 @@
|
|||
## Exemples de courbes de densité
|
||||
library(MASS)
|
||||
source("fonctions.r")
|
||||
dGAL1 <- function(x) dGALkappa(x,param=c(0,1,1,1))
|
||||
dGAL2 <- function(x) dGALkappa(x,param=c(0,1,2,1))
|
||||
dGAL3 <- function(x) dGALkappa(x,param=c(0,1,2,2))
|
||||
dGAL4 <- function(x) dGALkappa(x,param=c(0,1,.5,1))
|
||||
pdf("dGAL-exemples.pdf")
|
||||
curve(dGAL1,from=-5,to=5,n=500,xlab="y",ylab="f(y)")
|
||||
curve(dGAL2,from=-5,to=5,n=500,add=TRUE)
|
||||
curve(dGAL3,from=-5,to=5,n=500,add=TRUE)
|
||||
curve(dGAL4,from=-5,to=5,n=500,add=TRUE)
|
||||
points(-2,dGAL1(-2),pch=21)
|
||||
points(1,dGAL1(1),pch=21)
|
||||
points(-2,dGAL2(-2),pch=22)
|
||||
points(0.49,dGAL2(0.49),pch=22)
|
||||
points(-2,dGAL3(-2),pch=15)
|
||||
points(0.25,dGAL3(0.25),pch=15)
|
||||
points(-2,dGAL4(-2),pch=16)
|
||||
points(1.5,dGAL4(1.5),pch=16)
|
||||
pchgraph <- c(21,22,15,16)
|
||||
noms <- c("GAL(x; 0, 1, 1, 1)","GAL(x; 0, 1, 2, 1)","GAL(x; 0, 1, 2, 2)","GAL(x; 0, 1, 0.5, 1)")
|
||||
legend(-5, 0.7, noms, cex=1.0,
|
||||
pch=pchgraph, lty=1)
|
||||
dev.off()
|
||||
BIN
memoire/graphiques/increment1.dia
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BIN
memoire/graphiques/increment1.dia
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198
memoire/graphiques/increment1.tex
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198
memoire/graphiques/increment1.tex
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|
|
@ -0,0 +1,198 @@
|
|||
% Graphic for TeX using PGF
|
||||
% Title: /home/francois/projet-de-maitrise/graphiques/increment1.dia
|
||||
% Creator: Dia v0.97.2
|
||||
% CreationDate: Mon Jul 29 16:42:05 2013
|
||||
% For: francois
|
||||
% \usepackage{tikz}
|
||||
% The following commands are not supported in PSTricks at present
|
||||
% We define them conditionally, so when they are implemented,
|
||||
% this pgf file will use them.
|
||||
\ifx\du\undefined
|
||||
\newlength{\du}
|
||||
\fi
|
||||
\setlength{\du}{15\unitlength}
|
||||
\begin{tikzpicture}
|
||||
\pgftransformxscale{1.000000}
|
||||
\pgftransformyscale{-1.000000}
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\definecolor{dialinecolor}{rgb}{1.000000, 1.000000, 1.000000}
|
||||
\pgfsetfillcolor{dialinecolor}
|
||||
\pgfsetlinewidth{0.100000\du}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetbuttcap
|
||||
{
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetfillcolor{dialinecolor}
|
||||
% was here!!!
|
||||
\pgfsetarrowsend{stealth}
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\draw (19.200000\du,10.800000\du)--(28.800000\du,10.800000\du);
|
||||
}
|
||||
\pgfsetlinewidth{0.100000\du}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetbuttcap
|
||||
{
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetfillcolor{dialinecolor}
|
||||
% was here!!!
|
||||
\pgfsetarrowsend{stealth}
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\draw (19.200000\du,10.800000\du)--(19.200000\du,3.600000\du);
|
||||
}
|
||||
\pgfsetlinewidth{0.100000\du}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetbuttcap
|
||||
{
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetfillcolor{dialinecolor}
|
||||
% was here!!!
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\draw (20.400000\du,10.600000\du)--(20.400000\du,11.000000\du);
|
||||
}
|
||||
\pgfsetlinewidth{0.100000\du}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetbuttcap
|
||||
{
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetfillcolor{dialinecolor}
|
||||
% was here!!!
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\draw (26.400000\du,10.600000\du)--(26.400000\du,11.000000\du);
|
||||
}
|
||||
\pgfsetlinewidth{0.100000\du}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetbuttcap
|
||||
{
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetfillcolor{dialinecolor}
|
||||
% was here!!!
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\draw (19.000000\du,9.600000\du)--(19.400000\du,9.600000\du);
|
||||
}
|
||||
% setfont left to latex
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\node[anchor=west] at (20.200000\du,12.000000\du){0};
|
||||
% setfont left to latex
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\node[anchor=west] at (26.200000\du,12.000000\du){$T_1$};
|
||||
% setfont left to latex
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\node[anchor=west] at (18.200000\du,9.800000\du){0};
|
||||
% setfont left to latex
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\node[anchor=west] at (17.400000\du,6.200000\du){$X_1$};
|
||||
\pgfsetlinewidth{0.100000\du}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetbuttcap
|
||||
{
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetfillcolor{dialinecolor}
|
||||
% was here!!!
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\draw (19.000000\du,6.000000\du)--(19.400000\du,6.000000\du);
|
||||
}
|
||||
\pgfsetlinewidth{0.100000\du}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetbuttcap
|
||||
{
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetfillcolor{dialinecolor}
|
||||
% was here!!!
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\draw (26.200000\du,6.000000\du)--(27.400000\du,6.000000\du);
|
||||
}
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\draw (26.200000\du,6.000000\du)--(27.400000\du,6.000000\du);
|
||||
\pgfsetlinewidth{0.100000\du}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetmiterjoin
|
||||
\pgfsetbuttcap
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetfillcolor{dialinecolor}
|
||||
\pgfpathmoveto{\pgfpoint{26.200000\du}{6.000000\du}}
|
||||
\pgfpathcurveto{\pgfpoint{26.200000\du}{5.875000\du}}{\pgfpoint{26.325000\du}{5.750000\du}}{\pgfpoint{26.450000\du}{5.750000\du}}
|
||||
\pgfpathcurveto{\pgfpoint{26.575000\du}{5.750000\du}}{\pgfpoint{26.700000\du}{5.875000\du}}{\pgfpoint{26.700000\du}{6.000000\du}}
|
||||
\pgfpathcurveto{\pgfpoint{26.700000\du}{6.125000\du}}{\pgfpoint{26.575000\du}{6.250000\du}}{\pgfpoint{26.450000\du}{6.250000\du}}
|
||||
\pgfpathcurveto{\pgfpoint{26.325000\du}{6.250000\du}}{\pgfpoint{26.200000\du}{6.125000\du}}{\pgfpoint{26.200000\du}{6.000000\du}}
|
||||
\pgfusepath{fill}
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
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\pgfsetdash{}{0pt}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetmiterjoin
|
||||
\pgfsetbuttcap
|
||||
{
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetfillcolor{dialinecolor}
|
||||
% was here!!!
|
||||
{\pgfsetcornersarced{\pgfpoint{0.000000\du}{0.000000\du}}\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\draw (20.500000\du,-0.300000\du)--(20.500000\du,0.000000\du);
|
||||
}}
|
||||
\pgfsetlinewidth{0.100000\du}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetmiterjoin
|
||||
\pgfsetbuttcap
|
||||
{
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetfillcolor{dialinecolor}
|
||||
% was here!!!
|
||||
{\pgfsetcornersarced{\pgfpoint{0.000000\du}{0.000000\du}}\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\draw (20.900000\du,-0.200000\du)--(20.476079\du,-0.012490\du);
|
||||
}}
|
||||
\pgfsetlinewidth{0.100000\du}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetmiterjoin
|
||||
\pgfsetbuttcap
|
||||
{
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetfillcolor{dialinecolor}
|
||||
% was here!!!
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\pgfpathmoveto{\pgfpoint{19.000000\du}{0.025000\du}}
|
||||
\pgfpathcurveto{\pgfpoint{19.468950\du}{0.025000\du}}{\pgfpoint{19.200000\du}{0.925000\du}}{\pgfpoint{20.500000\du}{0.925000\du}}
|
||||
\pgfusepath{stroke}
|
||||
}
|
||||
\pgfsetlinewidth{0.100000\du}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetmiterjoin
|
||||
\pgfsetbuttcap
|
||||
{
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetfillcolor{dialinecolor}
|
||||
% was here!!!
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\pgfpathmoveto{\pgfpoint{21.500000\du}{0.925000\du}}
|
||||
\pgfpathcurveto{\pgfpoint{22.800000\du}{0.925000\du}}{\pgfpoint{22.558025\du}{0.025000\du}}{\pgfpoint{23.000000\du}{0.025000\du}}
|
||||
\pgfusepath{stroke}
|
||||
}
|
||||
\pgfsetlinewidth{0.100000\du}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetmiterjoin
|
||||
\pgfsetbuttcap
|
||||
{
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetfillcolor{dialinecolor}
|
||||
% was here!!!
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\pgfpathmoveto{\pgfpoint{20.500000\du}{0.925000\du}}
|
||||
\pgfpathcurveto{\pgfpoint{20.700000\du}{0.925000\du}}{\pgfpoint{21.000000\du}{1.125000\du}}{\pgfpoint{21.000000\du}{1.425000\du}}
|
||||
\pgfusepath{stroke}
|
||||
}
|
||||
\pgfsetlinewidth{0.100000\du}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetmiterjoin
|
||||
\pgfsetbuttcap
|
||||
{
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetfillcolor{dialinecolor}
|
||||
% was here!!!
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\pgfpathmoveto{\pgfpoint{21.500000\du}{0.925000\du}}
|
||||
\pgfpathcurveto{\pgfpoint{21.300000\du}{0.925000\du}}{\pgfpoint{21.000000\du}{1.125000\du}}{\pgfpoint{21.000000\du}{1.425000\du}}
|
||||
\pgfusepath{stroke}
|
||||
}
|
||||
% setfont left to latex
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\node[anchor=west] at (19.800000\du,2.175000\du){P(X>y)};
|
||||
% setfont left to latex
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\node[anchor=west] at (10.300000\du,-11.500000\du){f(x)};
|
||||
% setfont left to latex
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\node[anchor=west] at (23.400000\du,1.000000\du){x};
|
||||
% setfont left to latex
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\node[anchor=west] at (22.000000\du,1.000000\du){};
|
||||
\pgfsetlinewidth{0.100000\du}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetbuttcap
|
||||
{
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetfillcolor{dialinecolor}
|
||||
% was here!!!
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\draw (20.900000\du,-0.200000\du)--(20.900000\du,0.000000\du);
|
||||
}
|
||||
\end{tikzpicture}
|
||||
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Add table
Add a link
Reference in a new issue