77 lines
1.9 KiB
R
77 lines
1.9 KiB
R
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# Differenciation of the cumulant generating fonction of the
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# 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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#' 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
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#' of evaluation
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#'
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#' @author Francois Pelletier
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diffcgfGAL <- 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[2]^2*u*param[3]+
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2*param[3]^2+2*param[2]^2+param[2]^4*u^2)/
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(-2+param[2]^2*u^2+2*param[3]*u)^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]*(3*param[2]^4*u^2*param[3]+
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6*param[2]^2*u*param[3]^2+param[2]^6*u^3+
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6*param[2]^4*u+6*param[2]^2*param[3]+4*param[3]^3)/
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(-2+param[2]^2*u^2+2*param[3]*u)^3
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}
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if(order==4)
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{
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(12*param[2]^8*param[4]*u^4+48*param[3]*param[2]^6*param[4]*u^3+
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(144*param[2]^6+144*param[3]^2*param[2]^4)*param[4]*u^2+
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(288*param[3]*param[2]^4+192*param[3]^3*param[2]^2)*param[4]*u+
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(48*param[2]^4+192*param[3]^2*param[2]^2+96*param[3]^4)*param[4])/
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(param[2]^8*u^8+8*param[3]*param[2]^6*u^7+
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(24*param[3]^2*param[2]^4-8*param[2]^6)*u^6+
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(32*param[3]^3*param[2]^2-48*param[3]*param[2]^4)*u^5+
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(24*param[2]^4-96*param[3]^2*param[2]^2+16*param[3]^4)*u^4+
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(96*param[3]*param[2]^2-64*param[3]^3)*u^3+
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(96*param[3]^2-32*param[2]^2)*u^2+(-64)*param[3]*u+16)
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}
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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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}
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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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