87 lines
2.7 KiB
R
87 lines
2.7 KiB
R
# Derivative vector of the mean and standard deviation of 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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#' Derivative vector of the mean and standard deviation of GAL distribution
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#' @param param Parameter vector
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#' @param order 1 for mean, 2 for standard deviation
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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 vector of the derivative of the analytical moment
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#'
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#' @author Francois Pelletier
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dmGAL <- function(param,order,type="mu",log=FALSE)
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{ if(log)
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{
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eparam <- exp(param)
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if(order==1)
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{
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if(type=="mu")
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{
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c(1,0,eparam[4],eparam[3])
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}
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else if(type=="kappa")
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{
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c(1,
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-(1/2)*sqrt(2)*eparam[4]*(-1+eparam[3]^2)/eparam[3],
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-(1/2)*eparam[4]*eparam[2]*sqrt(2)*(eparam[3]^2+1)/eparam[3]^2,
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-(1/2)*sqrt(2)*eparam[2]*(-1+eparam[3]^2)/eparam[3])
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}
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}
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if(order==2)
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{
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if(type=="mu")
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{
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c(0,
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eparam[4]*eparam[2]/sqrt(eparam[4]*eparam[2]^2+eparam[4]*eparam[3]^2),
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eparam[4]*eparam[3]/sqrt(eparam[4]*eparam[2]^2+eparam[4]*eparam[3]^2),
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(1/2)*(eparam[2]^2+eparam[3]^2)/sqrt(eparam[4]*eparam[2]^2+eparam[4]*eparam[3]^2))
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}
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else if(type=="kappa")
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{
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c(0,
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(1/2)*sqrt(2)*eparam[4]*eparam[2]*(eparam[3]^4+1)/(sqrt(eparam[4]*eparam[2]^2*(eparam[3]^4+1)/eparam[3]^2)*eparam[3]^2),
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(1/2)*sqrt(2)*eparam[4]*eparam[2]^2*(eparam[3]^4-1)/(sqrt(eparam[4]*eparam[2]^2*(eparam[3]^4+1)/eparam[3]^2)*eparam[3]^3),
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(1/4)*sqrt(2)*eparam[2]^2*(eparam[3]^4+1)/(sqrt(eparam[4]*eparam[2]^2*(eparam[3]^4+1)/eparam[3]^2)*eparam[3]^2))
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}
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}
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}
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else
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{
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if(order==1)
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{
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if(type=="mu")
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{
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c(1,0,param[4],param[3])
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}
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else if(type=="kappa")
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{
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c(1,
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-(1/2)*sqrt(2)*param[4]*(-1+param[3]^2)/param[3],
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-(1/2)*param[4]*param[2]*sqrt(2)*(param[3]^2+1)/param[3]^2,
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-(1/2)*sqrt(2)*param[2]*(-1+param[3]^2)/param[3])
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}
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}
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if(order==2)
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{
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if(type=="mu")
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{
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c(0,
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param[4]*param[2]/sqrt(param[4]*param[2]^2+param[4]*param[3]^2),
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param[4]*param[3]/sqrt(param[4]*param[2]^2+param[4]*param[3]^2),
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(1/2)*(param[2]^2+param[3]^2)/sqrt(param[4]*param[2]^2+param[4]*param[3]^2))
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}
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else if(type=="kappa")
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{
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c(0,
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(1/2)*sqrt(2)*param[4]*param[2]*(param[3]^4+1)/(sqrt(param[4]*param[2]^2*(param[3]^4+1)/param[3]^2)*param[3]^2),
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(1/2)*sqrt(2)*param[4]*param[2]^2*(param[3]^4-1)/(sqrt(param[4]*param[2]^2*(param[3]^4+1)/param[3]^2)*param[3]^3),
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(1/4)*sqrt(2)*param[2]^2*(param[3]^4+1)/(sqrt(param[4]*param[2]^2*(param[3]^4+1)/param[3]^2)*param[3]^2))
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}
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}
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}
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}
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