Ajout de plusieurs fonctions
This commit is contained in:
François Pelletier
parent
bdf752111e
commit
473c634d72
11 changed files with 422 additions and 1 deletions
103
R/cmGAL.R
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103
R/cmGAL.R
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# Centered moments of the GAL distribution
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# Skewness and (adjusted) kurtosis of the GAL distribution
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#
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# Author: Francois Pelletier
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#
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# LGPL 3.0
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###############################################################################
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#' Centered moments of the GAL distribution
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#' @param order Order of raw moment
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#' @param param Parameter vector
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#' @param type Choose between "mu" or "kappa" parametrization
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#' @param log Logical for log-parameters
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#' @return A numeric value of the centered moment
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#'
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#' @author Francois Pelletier
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cmGAL <- function(order,param,type="mu",log=FALSE)
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{
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testparGAL(param,type,log)
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if(log)
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{
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cmGAL(order,exp(param),type,log=FALSE)
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}
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else
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{
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if(type=="mu")
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{
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if(order==2)
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{
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param[4]*param[2]^2+param[4]*param[3]^2
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}
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if(order==3)
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{
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3*param[3]*param[4]*param[2]^2+2*param[3]^3*param[4]
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}
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if(order==4)
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{
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(3*param[4]^2+3*param[4])*param[2]^4+(6*param[3]^2*param[4]^2+12*param[3]^2*param[4])*param[2]^2+3*param[3]^4*param[4]^2+6*param[3]^4*param[4]
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}
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else
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stop("order must be 2,3 or 4")
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}
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if(type=="kappa")
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{
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if(order==2)
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{
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(1/2)*param[4]*param[2]^2*(param[3]^4+1)/param[3]^2
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}
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if(order==3)
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{
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(1/2)*param[4]*param[2]^3*sqrt(2)*(1-param[3]^6)/param[3]^3
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}
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if(order==4)
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{
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(3/4)*param[4]*((param[4]+2)*param[3]^8+2*param[4]*param[3]^4+param[4]+2)*param[2]^4/param[3]^4
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}
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else
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stop("order must be 2,3 or 4")
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}
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}
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}
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#' Skewness of the GAL distribution
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#' @param param Parameter vector
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#' @param type Choose between "mu" or "kappa" parametrization
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#' @param log Logical for log-parameters
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#' @return A numeric value of the skewness
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#'
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#' @author Francois Pelletier
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skewnessGAL <- function(param,type="mu",log=FALSE)
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{
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testparGAL(param,type,log)
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if(log)
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{
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skewnessGAL(exp(param),type,log=FALSE)
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}
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else
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{
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cmGAL(3,param,type) / (cmGAL(2,param,type)^(3/2))
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}
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}
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#' (Adjusted) kurtosis of the GAL distribution
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#' @param param Parameter vector
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#' @param type Choose between "mu" or "kappa" parametrization
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#' @param log Logical for log-parameters
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#' @param adjust Logical to use the adjusted kurtosis
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#' @return A numeric value of the kurtosis
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#'
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#' @author Francois Pelletier
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kurtosisGAL <- function(param,type="mu",log=FALSE,adjust=TRUE)
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{
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testparGAL(param,type,log)
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if(log)
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{
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kurtosisGAL(exp(param),type,log=FALSE)
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}
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else
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{
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cmGAL(4,param,type) / (cmGAL(2,param,type)^2) - 3*adjust
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}
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}
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36
R/fgmGAL.R
36
R/fgmGAL.R
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@ -1,4 +1,5 @@
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# Moment generating function of GAL distribution
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# Cumulant generating function of GAL distribution
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#
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# Author: Francois Pelletier
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#
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@ -38,4 +39,39 @@ mgfGAL <- function(u,param,type="mu",log=FALSE)
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exp(param[1]*u)*((param[2]^2*u^2)/2+(param[3]*param[2]*u)/sqrt(2)-(param[2]*u)/(sqrt(2)*param[3])+1)^(-param[4])
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}
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}
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}
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#' Cumulant generating function of GAL distribution
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#' @param u Transform variate
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#' @param param Parameter vector
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#' @param type Choose between "mu" or "kappa" parametrization
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#' @param log Logical for log-parameters
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#' @return Cumulant generating function value at point u for given parameter vector
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#'
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#' @author Francois Pelletier
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cgfGAL <- function(u,param,type="mu",log=FALSE)
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{
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testparGAL(param,type,log)
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if(log)
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{
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if(type=="mu")
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{
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log(exp(exp(param[1])*u)*(1-(1/2)*exp(param[2])^2*u^2-exp(param[3])*u)^(-exp(param[4])))
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}
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if(type=="kappa")
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{
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log(exp(exp(param[1])*u)*((exp(param[2])^2*u^2)/2+(exp(param[3])*exp(param[2])*u)/sqrt(2)-(exp(param[2])*u)/(sqrt(2)*exp(param[3]))+1)^(-exp(param[4])))
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}
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}
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else
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{
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if(type=="mu")
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{
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log(exp(param[1]*u)*(1-(1/2)*param[2]^2*u^2-param[3]*u)^(-param[4]))
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}
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if(type=="kappa")
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{
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log(exp(param[1]*u)*((param[2]^2*u^2)/2+(param[3]*param[2]*u)/sqrt(2)-(param[2]*u)/(sqrt(2)*param[3])+1)^(-param[4]))
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}
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}
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}
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91
R/mGAL.R
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91
R/mGAL.R
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# Raw moments of the GAL distribution
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#
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# Author: Francois Pelletier
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#
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# LGPL 3.0
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###############################################################################
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#' Raw moments of the GAL distribution
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#' @param order Order of raw moment
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#' @param param Parameter vector
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#' @param type Choose between "mu" or "kappa" parametrization
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#' @param log Logical for log-parameters
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#' @return A numeric value of the raw moment
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#'
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#' @author Francois Pelletier
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mGAL <- function(order,param,type="mu",log=FALSE)
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{
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testparGAL(param,type,log)
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if(log)
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{
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mGAL(order,exp(param),type,log=FALSE)
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}
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else
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{
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if(type=="mu")
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{
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if(order==1)
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{
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param[1]+param[4]*param[3]
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}
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if(order==2)
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{
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param[1]^2+2*param[1]*param[4]*param[3]+param[4]^2*param[3]^2+
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param[4]*param[2]^2+param[4]*param[3]^2
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}
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if(order==3)
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{
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3*param[1]*param[4]*param[2]^2+3*param[1]^2*param[4]*param[3]+
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3*param[1]*param[4]^2*param[3]^2+param[1]^3+
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3*param[1]*param[4]*param[3]^2+param[4]^3*param[3]^3+
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3*param[4]^2*param[3]*param[2]^2+3*param[4]^2*param[3]^3+
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3*param[4]*param[2]^2*param[3]+2*param[4]*param[3]^3
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}
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if(order==4)
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{
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6*param[1]^2*param[4]*param[3]^2+18*param[4]^2*param[3]^2*param[2]^2+
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12*param[4]*param[2]^2*param[3]^2+
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12*param[1]*param[4]*param[2]^2*param[3]+4*param[1]^3*param[4]*param[3]+
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8*param[1]*param[4]*param[3]^3+12*param[1]*param[4]^2*param[3]*param[2]^2+
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6*param[1]^2*param[4]^2*param[3]^2+param[1]^4+
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6*param[1]^2*param[4]*param[2]^2+param[4]^4*param[3]^4+
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6*param[4]^3*param[3]^2*param[2]^2+6*param[4]^3*param[3]^4+
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3*param[4]^2*param[2]^4+11*param[4]^2*param[3]^4+
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3*param[4]*param[2]^4+6*param[4]*param[3]^4+
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12*param[1]*param[4]^2*param[3]^3+4*param[1]*param[4]^3*param[3]^3
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}
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else
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stop("order must be 1,2,3 or 4")
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}
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if(type=="kappa")
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{
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if(order==1)
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{
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(1/2)*(param[4]*param[2]*sqrt(2)-param[4]*param[2]*sqrt(2)*param[2]^2+2*param[1]*param[2])/param[2]
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}
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if(order==2)
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{
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(1/2)*(-2*param[1]*param[4]*param[2]*(param[2]+1)*(param[2]-1)*param[2]*sqrt(2)+
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param[4]*param[2]^2*(param[4]+1)*param[2]^4+(-2*param[4]^2*param[2]^2+2*param[1]^2)*param[2]^2+
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param[4]*param[2]^2*(param[4]+1))/param[2]^2
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}
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if(order==3)
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{
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(1/4)*(-(param[2]-1)*param[4]*param[2]*(param[2]+1)*(((-2*param[2]^2+1+param[2]^4)*param[4]+
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2*param[2]^2+2*param[2]^4+2)*(param[4]+1)*param[2]^2+
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6*param[1]^2*param[2]^2)*sqrt(2)+(6*(param[4]*((-2*param[2]^2+1+param[2]^4)*param[4]+
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param[2]^4+1)*param[2]^2+(2/3)*param[1]^2*param[2]^2))*
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param[2]*param[1])/param[2]^3
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}
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if(order==4)
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{
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1/4*(4*param[1]^4*param[2]^4+param[4]^4*param[2]^4+6*param[4]^3*param[2]^4+11*param[4]^2*param[2]^4+6*param[4]*param[2]^4-24*param[4]^2*param[2]^4*param[1]^2*param[2]^2+12*param[4]^2*param[2]^2*param[1]^2*param[2]^2+12*param[4]^2*param[2]^6*param[1]^2*param[2]^2+12*param[4]*param[2]^6*param[1]^2*param[2]^2-4*param[4]^4*param[2]^4*param[2]^2+6*param[4]^4*param[2]^4*param[2]^4-4*param[4]^4*param[2]^4*param[2]^6+param[4]^4*param[2]^4*param[2]^8-12*param[4]^3*param[2]^4*param[2]^2+12*param[4]^3*param[2]^4*param[2]^4-12*param[4]^3*param[2]^4*param[2]^6+6*param[4]^3*param[2]^4*param[2]^8+11*param[4]^2*param[2]^4*param[2]^8-8*param[4]^2*param[2]^4*param[2]^2+6*param[4]^2*param[2]^4*param[2]^4-8*param[4]^2*param[2]^4*param[2]^6+6*param[4]*param[2]^4*param[2]^8+12*param[4]*param[2]^2*param[1]^2*param[2]^2-12*param[4]^3*param[2]^3*param[2]^3*param[1]*2^(1/2)+4*param[4]^3*param[2]^3*param[2]*param[1]*2^(1/2)+12*param[4]^2*param[2]^3*param[2]*param[1]*2^(1/2)+12*param[4]^3*param[2]^3*param[2]^5*param[1]*2^(1/2)+12*param[4]^2*param[2]^3*param[2]^5*param[1]*2^(1/2)+8*param[4]*param[2]^3*param[2]*param[1]*2^(1/2)+8*param[4]*param[2]*param[2]^3*param[1]^3*2^(1/2)-12*param[4]^2*param[2]^3*param[2]^3*param[1]*2^(1/2)-4*param[4]^3*param[2]^3*param[2]^7*param[1]*2^(1/2)-12*param[4]^2*param[2]^3*param[2]^7*param[1]*2^(1/2)-8*param[4]*param[2]^3*param[2]^7*param[1]*2^(1/2)-8*param[4]*param[2]*param[2]^5*param[1]^3*2^(1/2))/param[2]^4
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}
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else
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stop("order must be 1,2,3 or 4")
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}
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}
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}
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36
R/riskneutralparGAL.R
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36
R/riskneutralparGAL.R
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# Risk neutral conversion of parameters of GAL distirbution
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#
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# Author: Francois Pelletier
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#
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# LGPL 3.0
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###############################################################################
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#' Risk neutral conversion of parameters of GAL distirbution
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#' @param param Parameter vector
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#' @param riskfree Risk-free rate
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#' @param type Choose between "mu" or "kappa" parametrization
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#' @param log Logical for log-parameters
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#' @return Risk neutral parameter vector
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#'
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#' @author Francois Pelletier
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riskneutralparGAL <- function(param,riskfree,type="mu",log=FALSE)
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{
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testparGAL(param,type,log)
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if(type=="kappa")
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{
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riskneutralparGAL(changetypeGAL(param,type="kappa",target="mu"),riskfree,type="mu",log)
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}
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if(type=="mu")
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{
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if(log)
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{
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c(log(riskfree+log(1-exp(param[3])-exp(param[2])^2/2)*param[4]),param[2],param[3],param[4])
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}
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else
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{
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c(riskfree+log(1-param[3]-param[2]^2/2)*param[4],param[2],param[3],param[4])
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}
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}
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}
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#' Check for the validity of a parameter vector. Stop at error.
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#' @param param Parameter vector
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#' @param type Choose between "mu" or "kappa" parametrization
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#' @param log Logical for log-parameters
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#' @param log Logical for log-parameters
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#' @return logical
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#'
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#' @author Francois Pelletier
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27
man/cgfGAL.Rd
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27
man/cgfGAL.Rd
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\name{cgfGAL}
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\alias{cgfGAL}
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\title{Cumulant generating function of GAL distribution}
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\usage{
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cgfGAL(u, param, type = "mu", log = FALSE)
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}
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\arguments{
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\item{u}{Transform variate}
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\item{param}{Parameter vector}
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\item{type}{Choose between "mu" or "kappa"
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parametrization}
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\item{log}{Logical for log-parameters}
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}
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\value{
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Cumulant generating function value at point u for given
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parameter vector
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}
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\description{
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Cumulant generating function of GAL distribution
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}
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\author{
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Francois Pelletier
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}
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26
man/cmGAL.Rd
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26
man/cmGAL.Rd
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\name{cmGAL}
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\alias{cmGAL}
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\title{Centered moments of the GAL distribution}
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\usage{
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cmGAL(order, param, type = "mu", log = FALSE)
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}
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\arguments{
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\item{order}{Order of raw moment}
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\item{param}{Parameter vector}
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\item{type}{Choose between "mu" or "kappa"
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parametrization}
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\item{log}{Logical for log-parameters}
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}
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\value{
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A numeric value of the centered moment
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}
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\description{
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Centered moments of the GAL distribution
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}
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\author{
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Francois Pelletier
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}
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26
man/kurtosisGAL.Rd
Normal file
26
man/kurtosisGAL.Rd
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\name{kurtosisGAL}
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\alias{kurtosisGAL}
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\title{(Adjusted) kurtosis of the GAL distribution}
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\usage{
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kurtosisGAL(param, type = "mu", log = FALSE, adjust = TRUE)
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}
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\arguments{
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\item{param}{Parameter vector}
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\item{type}{Choose between "mu" or "kappa"
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parametrization}
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\item{log}{Logical for log-parameters}
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\item{adjust}{Logical to use the adjusted kurtosis}
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}
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\value{
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A numeric value of the kurtosis
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}
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\description{
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(Adjusted) kurtosis of the GAL distribution
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}
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\author{
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Francois Pelletier
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}
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26
man/mGAL.Rd
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26
man/mGAL.Rd
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\name{mGAL}
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\alias{mGAL}
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\title{Raw moments of the GAL distribution}
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\usage{
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mGAL(order, param, type = "mu", log = FALSE)
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}
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\arguments{
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\item{order}{Order of raw moment}
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\item{param}{Parameter vector}
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\item{type}{Choose between "mu" or "kappa"
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parametrization}
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\item{log}{Logical for log-parameters}
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}
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\value{
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A numeric value of the raw moment
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}
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\description{
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Raw moments of the GAL distribution
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}
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\author{
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Francois Pelletier
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}
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26
man/riskneutralparGAL.Rd
Normal file
26
man/riskneutralparGAL.Rd
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\name{riskneutralparGAL}
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\alias{riskneutralparGAL}
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\title{Risk neutral conversion of parameters of GAL distirbution}
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\usage{
|
||||
riskneutralparGAL(param, riskfree, type = "mu", log = FALSE)
|
||||
}
|
||||
\arguments{
|
||||
\item{param}{Parameter vector}
|
||||
|
||||
\item{riskfree}{Risk-free rate}
|
||||
|
||||
\item{type}{Choose between "mu" or "kappa"
|
||||
parametrization}
|
||||
|
||||
\item{log}{Logical for log-parameters}
|
||||
}
|
||||
\value{
|
||||
Risk neutral parameter vector
|
||||
}
|
||||
\description{
|
||||
Risk neutral conversion of parameters of GAL distirbution
|
||||
}
|
||||
\author{
|
||||
Francois Pelletier
|
||||
}
|
||||
|
||||
24
man/skewnessGAL.Rd
Normal file
24
man/skewnessGAL.Rd
Normal file
|
|
@ -0,0 +1,24 @@
|
|||
\name{skewnessGAL}
|
||||
\alias{skewnessGAL}
|
||||
\title{Skewness of the GAL distribution}
|
||||
\usage{
|
||||
skewnessGAL(param, type = "mu", log = FALSE)
|
||||
}
|
||||
\arguments{
|
||||
\item{param}{Parameter vector}
|
||||
|
||||
\item{type}{Choose between "mu" or "kappa"
|
||||
parametrization}
|
||||
|
||||
\item{log}{Logical for log-parameters}
|
||||
}
|
||||
\value{
|
||||
A numeric value of the skewness
|
||||
}
|
||||
\description{
|
||||
Skewness of the GAL distribution
|
||||
}
|
||||
\author{
|
||||
Francois Pelletier
|
||||
}
|
||||
|
||||
Loading…
Reference in a new issue