33 lines
1.1 KiB
R
33 lines
1.1 KiB
R
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# Saddlepoint approximation of the distribution function of the Esscher
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# transform 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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#' Saddlepoint approximation of the distribution function of the Esscher
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#' transform of the GAL distribution
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#' @param x vector of quantiles
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#' @param param Parameter vector
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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 Saddlepoint approximation of the distribution function
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psaddleapproxEsscherGAL <- function(x,param,eval.time=1,type="mu",log=FALSE)
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{
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s <- saddlepointEsscherGAL(x,param,eval.time,type,log)
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u <- s * sqrt(diffcgfEsscherGAL(s,2,param,eval.time,type,log))
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w <- sign(s)*sqrt(2*(s*x-cgfEsscherGAL(s,param,type,log)))
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if(x==mGAL(1,param,type,log))
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{
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1/2 + diffcgfEsscherGAL(0,3,param,eval.time,type,log)/
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(6*sqrt(2*pi)*diffcgfEsscherGAL(0,2,param,eval.time,type,log)^(3/2))
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}
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else
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{
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pnorm(w)+dnorm(w)*(1/w-1/u)
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}
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}
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