Nothing
###################################################################################
#kurtosis --- code due to G. Jay Kerns, gkerns@ysu.edu
###################################################################################
setMethod("kurtosis", signature(x = "Pareto"),
function(x, ...){
dots <- match.call(call = sys.call(sys.parent(1)),
expand.dots = FALSE)$"..."
fun <- NULL; cond <- NULL; low <- NULL; upp <- NULL
if(hasArg(low)) low <- dots$low
if(hasArg(upp)) upp <- dots$upp
if(hasArg(fun)||hasArg(cond)||!is.null(low)||!is.null(upp))
return(kurtosis(as(x,"AbscontDistribution"),...))
else{
a <- shape(x)
if(a<=4) return(NA)
else
return( 6*(a^3+a^2-6*a-2)/a/(a-3)/(a-4) )
}
})
### source http://mathworld.wolfram.com/ParetoDistribution.html
setMethod("kurtosis", signature(x = "Gumbel"),
function(x, ...){
dots <- match.call(call = sys.call(sys.parent(1)),
expand.dots = FALSE)$"..."
fun <- NULL; cond <- NULL; low <- NULL; upp <- NULL
if(hasArg(low)) low <- dots$low
if(hasArg(upp)) upp <- dots$upp
if(hasArg(fun)||hasArg(cond)||!is.null(low)||!is.null(upp))
return(kurtosis(as(x,"AbscontDistribution"),...))
else{
return(12/5)
# http://mathworld.wolfram.com/GumbelDistribution.html
}
})
setMethod("kurtosis", signature(x = "GPareto"),
function(x, ...){
dots <- match.call(call = sys.call(sys.parent(1)),
expand.dots = FALSE)$"..."
fun <- NULL; cond <- NULL; low <- NULL; upp <- NULL
if(hasArg(low)) low <- dots$low
if(hasArg(upp)) upp <- dots$upp
if(hasArg(fun)||hasArg(cond)||!is.null(low)||!is.null(upp))
return(kurtosis(as(x,"AbscontDistribution"),...))
else{
k <- shape(x)
if(k>=1/4) return(NA)
else
return( 3*(3+k+2*k^2)*(1-2*k)/(1-4*k)/(1-3*k)-3)
}
})
### source Maple ...
setMethod("kurtosis", signature(x = "GEV"),
function(x, ...){
dots <- match.call(call = sys.call(sys.parent(1)),
expand.dots = FALSE)$"..."
fun <- NULL; cond <- NULL; low <- NULL; upp <- NULL
if(hasArg(low)) low <- dots$low
if(hasArg(upp)) upp <- dots$upp
if(hasArg(fun)||hasArg(cond)||!is.null(low)||!is.null(upp))
return(kurtosis(as(x,"AbscontDistribution"),...))
else{
xi <- shape(x)
if(xi>=1/4) return(NA)
if(xi==0) return(12/5)
else
return((gamma(1-4*xi)- 4*gamma(1-xi)*gamma(1-3*xi)+6*gamma(1-2*xi)*gamma(1-xi)^2 - 3*gamma(1-xi)^4)/(gamma(1-2*xi)-gamma(1-xi)^2)^(2))
}
})
### source http://en.wikipedia.org/wiki/Generalized_extreme_value_distribution
### http://en.wikipedia.org/wiki/Gumbel_distribution
### http://en.wikipedia.org/wiki/Riemann_zeta_function
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