60 lines
1.6 KiB
R
60 lines
1.6 KiB
R
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# Differenciation of the cumulant generating fonction of the
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# Esscher transform with parameter 1 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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#' Differenciation of the cumulant generating fonction of the
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#' Esscher transform with parameter 1 of the GAL distribution
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#' @param u Transform variate point of evaluation
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#' @param order Order of differenciation
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#' @param param Parameters of the GAL distirbution
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#' @param eval.time Time of the process
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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 The value of the derivative at the transform variate point of evaluation
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#'
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#' @author Francois Pelletier
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diffcgfEsscherGAL <- function(u,order,param,eval.time=1,type="mu",log=FALSE)
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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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}
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if(order==2)
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{
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2*eval.time*param[4]*(2*param[3]^2+param[2]^4+2*param[2]^2+param[2]^4*u^2+2*param[2]^2*u*param[3]+2*param[3]*param[2]^2+2*param[2]^4*u)/(-2+param[2]^2*u^2+2*param[2]^2*u+param[2]^2+2*param[3]*u+2*param[3])^2
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}
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if(order==3)
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{
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-4*eval.time*param[4]*(6*param[2]^4+param[2]^6+3*param[2]^4*u^2*param[3]+6*param[2]^4*u*param[3]+6*param[2]^2*u*param[3]^2+4*param[3]^3+6*param[3]*param[2]^2+6*param[2]^4*u+param[2]^6*u^3+3*param[2]^6*u^2+3*param[2]^6*u+3*param[2]^4*param[3]+6*param[2]^2*param[3]^2)/(-2+param[2]^2*u^2+2*param[2]^2*u+param[2]^2+2*param[3]*u+2*param[3])^3
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}
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if(order==4)
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{
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}
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}
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else if(type=="kappa")
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{
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if(order==1)
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{
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}
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if(order==2)
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{
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}
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if(order==3)
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{
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}
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if(order==4)
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{
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}
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}
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}
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