36 lines
1.2 KiB
R
36 lines
1.2 KiB
R
# Evaluation of the saddlepoint of the Esscher transform with
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# parameter 1 of the GAL distribution for given quantiles
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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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#' Evaluation of the saddlepoint of the Esscher transform with
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#' parameter 1 of the GAL distribution for given quantiles
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#' @param x vector of quantiles
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#' @param param Parameters of the underlying GAL distribution
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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 saddlepoint for each point of the vector of quantiles
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#'
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#' @author Francois Pelletier
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saddlepointEsscherGAL <- function(x,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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(-eval.time*param[1]*param[2]^2+eval.time*param[4]*param[2]^2+x*param[2]^2-
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eval.time*param[1]*param[3]+x*param[3]-
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sqrt(eval.time^2*param[1]^2*param[3]^2-2*eval.time*param[1]*param[3]^2*x+
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eval.time^2*param[4]^2*param[2]^4+x^2*param[3]^2+
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2*eval.time^2*param[1]^2*param[2]^2-
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4*eval.time*param[1]*param[2]^2*x+2*x^2*param[2]^2))/
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(param[2]^2*(eval.time*param[1]-x))
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}
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else if (type=="kappa")
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{
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}
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}
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