103 lines
2.4 KiB
R
103 lines
2.4 KiB
R
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# Centered moments of the GAL distribution
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# Skewness and (adjusted) kurtosis 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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#' Centered moments of the GAL distribution
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#' @param order Order of raw moment
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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 A numeric value of the centered moment
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#'
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#' @author Francois Pelletier
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cmGAL <- function(order,param,type="mu",log=FALSE)
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{
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testparGAL(param,type,log)
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if(log)
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{
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cmGAL(order,exp(param),type,log=FALSE)
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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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if(order==2)
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{
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param[4]*param[2]^2+param[4]*param[3]^2
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}
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if(order==3)
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{
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3*param[3]*param[4]*param[2]^2+2*param[3]^3*param[4]
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}
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if(order==4)
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{
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(3*param[4]^2+3*param[4])*param[2]^4+(6*param[3]^2*param[4]^2+12*param[3]^2*param[4])*param[2]^2+3*param[3]^4*param[4]^2+6*param[3]^4*param[4]
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}
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else
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stop("order must be 2,3 or 4")
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}
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if(type=="kappa")
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{
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if(order==2)
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{
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(1/2)*param[4]*param[2]^2*(param[3]^4+1)/param[3]^2
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}
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if(order==3)
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{
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(1/2)*param[4]*param[2]^3*sqrt(2)*(1-param[3]^6)/param[3]^3
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}
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if(order==4)
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{
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(3/4)*param[4]*((param[4]+2)*param[3]^8+2*param[4]*param[3]^4+param[4]+2)*param[2]^4/param[3]^4
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}
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else
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stop("order must be 2,3 or 4")
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}
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}
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}
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#' Skewness of the GAL distribution
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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 A numeric value of the skewness
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#'
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#' @author Francois Pelletier
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skewnessGAL <- function(param,type="mu",log=FALSE)
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{
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testparGAL(param,type,log)
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if(log)
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{
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skewnessGAL(exp(param),type,log=FALSE)
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}
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else
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{
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cmGAL(3,param,type) / (cmGAL(2,param,type)^(3/2))
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}
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}
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#' (Adjusted) kurtosis of the GAL distribution
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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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#' @param adjust Logical to use the adjusted kurtosis
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#' @return A numeric value of the kurtosis
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#'
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#' @author Francois Pelletier
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kurtosisGAL <- function(param,type="mu",log=FALSE,adjust=TRUE)
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{
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testparGAL(param,type,log)
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if(log)
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{
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kurtosisGAL(exp(param),type,log=FALSE)
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}
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else
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{
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cmGAL(4,param,type) / (cmGAL(2,param,type)^2) - 3*adjust
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}
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}
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