92 lines
4.1 KiB
R
92 lines
4.1 KiB
R
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# Raw moments 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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#' Raw 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 raw moment
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#'
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#' @author Francois Pelletier
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mGAL <- 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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mGAL(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==1)
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{
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param[1]+param[4]*param[3]
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}
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if(order==2)
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{
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param[1]^2+2*param[1]*param[4]*param[3]+param[4]^2*param[3]^2+
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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[1]*param[4]*param[2]^2+3*param[1]^2*param[4]*param[3]+
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3*param[1]*param[4]^2*param[3]^2+param[1]^3+
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3*param[1]*param[4]*param[3]^2+param[4]^3*param[3]^3+
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3*param[4]^2*param[3]*param[2]^2+3*param[4]^2*param[3]^3+
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3*param[4]*param[2]^2*param[3]+2*param[4]*param[3]^3
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}
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if(order==4)
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{
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6*param[1]^2*param[4]*param[3]^2+18*param[4]^2*param[3]^2*param[2]^2+
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12*param[4]*param[2]^2*param[3]^2+
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12*param[1]*param[4]*param[2]^2*param[3]+4*param[1]^3*param[4]*param[3]+
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8*param[1]*param[4]*param[3]^3+12*param[1]*param[4]^2*param[3]*param[2]^2+
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6*param[1]^2*param[4]^2*param[3]^2+param[1]^4+
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6*param[1]^2*param[4]*param[2]^2+param[4]^4*param[3]^4+
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6*param[4]^3*param[3]^2*param[2]^2+6*param[4]^3*param[3]^4+
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3*param[4]^2*param[2]^4+11*param[4]^2*param[3]^4+
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3*param[4]*param[2]^4+6*param[4]*param[3]^4+
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12*param[1]*param[4]^2*param[3]^3+4*param[1]*param[4]^3*param[3]^3
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}
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else
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stop("order must be 1,2,3 or 4")
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}
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if(type=="kappa")
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{
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if(order==1)
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{
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(1/2)*(param[4]*param[2]*sqrt(2)-param[4]*param[2]*sqrt(2)*param[2]^2+2*param[1]*param[2])/param[2]
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}
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if(order==2)
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{
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(1/2)*(-2*param[1]*param[4]*param[2]*(param[2]+1)*(param[2]-1)*param[2]*sqrt(2)+
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param[4]*param[2]^2*(param[4]+1)*param[2]^4+(-2*param[4]^2*param[2]^2+2*param[1]^2)*param[2]^2+
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param[4]*param[2]^2*(param[4]+1))/param[2]^2
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}
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if(order==3)
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{
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(1/4)*(-(param[2]-1)*param[4]*param[2]*(param[2]+1)*(((-2*param[2]^2+1+param[2]^4)*param[4]+
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2*param[2]^2+2*param[2]^4+2)*(param[4]+1)*param[2]^2+
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6*param[1]^2*param[2]^2)*sqrt(2)+(6*(param[4]*((-2*param[2]^2+1+param[2]^4)*param[4]+
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param[2]^4+1)*param[2]^2+(2/3)*param[1]^2*param[2]^2))*
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param[2]*param[1])/param[2]^3
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}
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if(order==4)
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{
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1/4*(4*param[1]^4*param[2]^4+param[4]^4*param[2]^4+6*param[4]^3*param[2]^4+11*param[4]^2*param[2]^4+6*param[4]*param[2]^4-24*param[4]^2*param[2]^4*param[1]^2*param[2]^2+12*param[4]^2*param[2]^2*param[1]^2*param[2]^2+12*param[4]^2*param[2]^6*param[1]^2*param[2]^2+12*param[4]*param[2]^6*param[1]^2*param[2]^2-4*param[4]^4*param[2]^4*param[2]^2+6*param[4]^4*param[2]^4*param[2]^4-4*param[4]^4*param[2]^4*param[2]^6+param[4]^4*param[2]^4*param[2]^8-12*param[4]^3*param[2]^4*param[2]^2+12*param[4]^3*param[2]^4*param[2]^4-12*param[4]^3*param[2]^4*param[2]^6+6*param[4]^3*param[2]^4*param[2]^8+11*param[4]^2*param[2]^4*param[2]^8-8*param[4]^2*param[2]^4*param[2]^2+6*param[4]^2*param[2]^4*param[2]^4-8*param[4]^2*param[2]^4*param[2]^6+6*param[4]*param[2]^4*param[2]^8+12*param[4]*param[2]^2*param[1]^2*param[2]^2-12*param[4]^3*param[2]^3*param[2]^3*param[1]*2^(1/2)+4*param[4]^3*param[2]^3*param[2]*param[1]*2^(1/2)+12*param[4]^2*param[2]^3*param[2]*param[1]*2^(1/2)+12*param[4]^3*param[2]^3*param[2]^5*param[1]*2^(1/2)+12*param[4]^2*param[2]^3*param[2]^5*param[1]*2^(1/2)+8*param[4]*param[2]^3*param[2]*param[1]*2^(1/2)+8*param[4]*param[2]*param[2]^3*param[1]^3*2^(1/2)-12*param[4]^2*param[2]^3*param[2]^3*param[1]*2^(1/2)-4*param[4]^3*param[2]^3*param[2]^7*param[1]*2^(1/2)-12*param[4]^2*param[2]^3*param[2]^7*param[1]*2^(1/2)-8*param[4]*param[2]^3*param[2]^7*param[1]*2^(1/2)-8*param[4]*param[2]*param[2]^5*param[1]^3*2^(1/2))/param[2]^4
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}
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else
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stop("order must be 1,2,3 or 4")
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}
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}
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}
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