2014-01-03 06:40:46 +00:00
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# Moment generating function 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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#' Moment 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 Moment 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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mgfGAL <- function(u,param,type="mu",log=FALSE)
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{
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2014-01-04 18:02:45 +00:00
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testparGAL(param,type,log)
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2014-01-03 06:40:46 +00:00
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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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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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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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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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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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