Nothing
###################################################################################
#skewness --- code due to G. Jay Kerns, gkerns@ysu.edu
###################################################################################
setMethod("skewness", signature(x = "UnivariateDistribution"),
function(x, fun = function(t) {t}, cond, withCond = FALSE, useApply = TRUE, ...){
if(missing(cond)&&missing(fun)){
if(is(Symmetry(x),"SphericalSymmetry"))
return(0)
}
f2 <- function(t) {fun(t)^2}
f3 <- function(t) {fun(t)^3}
if(missing(cond))
{
m <- E(x, fun = fun, useApply = useApply, ...)
m2 <- E(x, fun = f2, useApply = useApply, ...)
m3 <- E(x, fun = f3, useApply = useApply, ...)
return( (m3-3*m2*m+2*m^3)/(var(x, fun = fun, useApply = TRUE, ...))^1.5 )
}
else{
m <- E(x, cond = cond, fun = fun, withCond = withCond, useApply = useApply, ...)
m2 <- E(x, cond = cond, fun = f2, withCond = withCond, useApply = useApply, ...)
m3 <- E(x, cond = cond, fun = f3, withCond = withCond, useApply = useApply, ...)
return( (m3-3*m2*m+2*m^3)/(var(x, fun = fun, cond = cond, withCond = FALSE, useApply = TRUE,...))^1.5 )
}
})
setMethod("skewness", signature(x = "AffLinDistribution"),
function(x, fun = function(t) {t}, cond, withCond = FALSE, useApply = TRUE, ...){
if (missing(fun) && missing(cond)){
return(sign(x@a)*skewness(x@X0, withCond = withCond, useApply = useApply,
...))
}
else return(skewness(x = as(x, sub("AffLin","",class(x))),
fun = fun, cond = cond, withCond = withCond,
useApply = useApply, ... ))
})
setMethod("skewness", signature(x = "AffLinAbscontDistribution"),
getMethod("skewness", signature(x = "AffLinDistribution")))
setMethod("skewness", signature(x = "AffLinDiscreteDistribution"),
getMethod("skewness", signature(x = "AffLinDistribution")))
setMethod("skewness", signature(x = "AffLinLatticeDistribution"),
getMethod("skewness", signature(x = "AffLinDistribution")))
###
# some exact skewnesses:
###
#
setMethod("skewness", signature(x = "Norm"),
function(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...){
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$upp
if(hasArg(fun)||hasArg(cond)||!is.null(low)||!is.null(upp))
return(skewness(as(x,"AbscontDistribution"),...))
else
return(0)
})
#
setMethod("skewness", signature(x = "Binom"),
function(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...){
dots <- match.call(call = sys.call(sys.parent(1)),
expand.dots = FALSE)$"..."
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(skewness(as(x,"DiscreteDistribution"),...))
else{
ret.v <- (1-2*prob(x))/sqrt(size(x)*prob(x)*(1-prob(x)))
if(!propagate.names){names(ret.v) <- NULL}
return(ret.v)
}
})
### source: https://mathworld.wolfram.com/BinomialDistribution.html
#
setMethod("skewness", signature(x = "Cauchy"),
function(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...){
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$upp
if(hasArg(fun)||hasArg(cond)||!is.null(low)||!is.null(upp))
return(skewness(as(x,"AbscontDistribution"),...))
else
return(NA)
})
### source https://mathworld.wolfram.com/CauchyDistribution.html
#
setMethod("skewness", signature(x = "Chisq"),
function(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...){
dots <- match.call(call = sys.call(sys.parent(1)),
expand.dots = FALSE)$"..."
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(skewness(as(x,"AbscontDistribution"),...))
else{
ret.v <- sqrt(8)*(df(x)+3*ncp(x))/(df(x)+2*ncp(x))^1.5
if(!propagate.names){names(ret.v) <- NULL}
return(ret.v)
}
})
### source https://mathworld.wolfram.com/Chi-SquaredDistribution.html
#
setMethod("skewness", signature(x = "Dirac"),
function(x, ...){return(NA)})
#
setMethod("skewness", signature(x = "DExp"),
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$upp
if(hasArg(fun)||hasArg(cond)||!is.null(low)||!is.null(upp))
return(skewness(as(x,"AbscontDistribution"),...))
else
return(0)
})
### source https://mathworld.wolfram.com/LaplaceDistribution.html
#
setMethod("skewness", signature(x = "Exp"),
function(x, ...){
dots <- match.call(call = sys.call(sys.parent(1)),
expand.dots = FALSE)$"..."
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(skewness(as(x,"AbscontDistribution"),...))
else
return(2)
})
### source https://mathworld.wolfram.com/ExponentialDistribution.html
#
setMethod("skewness", signature(x = "Fd"),
function(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...){
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$upp
if(hasArg(fun)||hasArg(cond)||!is.null(low)||!is.null(upp)) {
return(skewness(as(x,"AbscontDistribution"),...))
}else {
if (df2(x)>6){
m <- df1(x)
n <- df2(x)
d <- ncp(x)
#L <- d/m
#m2 <- 2*n^2*(m+n-2)/m/(n-2)^2/(n-4)*(1+2*L+m*L^2/(m+n-2))
m2 <- var(x)
m1 <- E(x)
m3 <- (n/m)^3/(n-2)/(n-4)/(n-6)*
(m^3+6*m^2+8*m+3*d*(m^2+6*m+8)+3*d^2*(m+4)+d^3)
# a <- 8*n^3*(m+n-2)*(2*m+n-2)/m^2/(n-2)^3/(n-4)/(n-6)
# b <- 1+3*L+6*m*L^2/(2*m+n-2)+2*m^2*L^3/(m+n-2)/(2*m+n-2)
ret.v <- (m3-3*m2*m1-m1^3)/m2^1.5
if(!propagate.names){names(ret.v) <- NULL}
return(ret.v)
} else {
return(NA)
}
}
})
### source (without ncp) https://mathworld.wolfram.com/F-Distribution.html
#
setMethod("skewness", signature(x = "Gammad"),
function(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...){
dots <- match.call(call = sys.call(sys.parent(1)),
expand.dots = FALSE)$"..."
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(skewness(as(x,"AbscontDistribution"),...))
else{
ret.v <- 2/sqrt(shape(x))
if(!propagate.names){names(ret.v) <- NULL}
return(ret.v)
}})
### source https://mathworld.wolfram.com/GammaDistribution.html
#
setMethod("skewness", signature(x = "Geom"),
function(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...){
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$upp
if(hasArg(fun)||hasArg(cond)||!is.null(low)||!is.null(upp))
return(skewness(as(x,"DiscreteDistribution"),...))
else{
p <- prob(x)
ret.v <- (2-p)/sqrt(1-p)
if(!propagate.names){names(ret.v) <- NULL}
return(ret.v)
}
})
### source https://mathworld.wolfram.com/GeometricDistribution.html
#
setMethod("skewness", signature(x = "Hyper"),
function(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...){
dots <- match.call(call = sys.call(sys.parent(1)),
expand.dots = FALSE)$"..."
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(skewness(as(x,"DiscreteDistribution"),...))
else
{k <- k(x)
m <- m(x)
n <- n(x)
ret.v <- sqrt((m+n-1)/(k*m*n)/(m+n-k))*(n-m)*(m+n-2*k)/(m+n-2)
if(!propagate.names){names(ret.v) <- NULL}
return(ret.v)
}
})
### source https://mathworld.wolfram.com/HypergeometricDistribution.html
#
setMethod("skewness", signature(x = "Logis"),
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$upp
if(hasArg(fun)||hasArg(cond)||!is.null(low)||!is.null(upp))
return(skewness(as(x,"AbscontDistribution"),...))
else
return(0)
})
### source https://mathworld.wolfram.com/LogisticDistribution.html
#
setMethod("skewness", signature(x = "Lnorm"),
function(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...){
dots <- match.call(call = sys.call(sys.parent(1)),
expand.dots = FALSE)$"..."
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(skewness(as(x,"AbscontDistribution"),...))
} else {
w <- exp(sdlog(x)^2)
ret.v <- sqrt(w-1)*(w+2)
if(!propagate.names){names(ret.v) <- NULL}
return(ret.v)
}
})
### source https://mathworld.wolfram.com/LogNormalDistribution.html
#
setMethod("skewness", signature(x = "Nbinom"),
function(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...){
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$upp
if(hasArg(fun)||hasArg(cond)||!is.null(low)||!is.null(upp))
return(skewness(as(x,"DiscreteDistribution"),...))
else{
p <- prob(x)
ret.v <- (2-p)/sqrt((1-p)*size(x))
if(!propagate.names){names(ret.v) <- NULL}
return(ret.v)
}
})
### source https://mathworld.wolfram.com/NegativeBinomialDistribution.html
#
setMethod("skewness", signature(x = "Pois"),
function(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...){
dots <- match.call(call = sys.call(sys.parent(1)),
expand.dots = FALSE)$"..."
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(skewness(as(x,"DiscreteDistribution"),...))
else{
ret.v <- 1/sqrt(lambda(x))
if(!propagate.names){names(ret.v) <- NULL}
return(ret.v)
}
})
### source https://mathworld.wolfram.com/PoissonDistribution.html
#
setMethod("skewness", signature(x = "Td"),
function(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...){
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$upp
if(hasArg(fun)||hasArg(cond)||!is.null(low)||!is.null(upp)) {
return(skewness(as(x,"AbscontDistribution"),...))
} else {
if (df(x)>3){
n <- df(x); d<- ncp(x)
m1 <- E(x)
m2 <- var(x)
m3 <- (n/2)^1.5*(3*d+d^3)*exp(lgamma((n-3)/2)-lgamma(n/2))
ret.v <- (m3-3*m2*m1-m1^3)/m2^1.5
if(!propagate.names){names(ret.v) <- NULL}
return(ret.v)
} else {
return(NA)
}
}
})
### source https://mathworld.wolfram.com/NoncentralStudentst-Distribution.html
#
setMethod("skewness", signature(x = "Unif"),
function(x, ...){
dots <- match.call(call = sys.call(sys.parent(1)),
expand.dots = FALSE)$"..."
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(skewness(as(x,"AbscontDistribution"),...))
else
return(0)
})
### source https://mathworld.wolfram.com/UniformDistribution.html
#
setMethod("skewness", signature(x = "Weibull"),
function(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...){
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$upp
if(hasArg(fun)||hasArg(cond)||!is.null(low)||!is.null(upp))
return(skewness(as(x,"AbscontDistribution"),...))
else{
g1 <- gamma(1+1/shape(x))
g2 <- gamma(1+2/shape(x))
g3 <- gamma(1+3/shape(x))
ret.v <- (g3-3*g1*(g2-g1^2)-g1^3)/(g2-g1^2)^1.5
if(!propagate.names){names(ret.v) <- NULL}
return(ret.v) }
})
### source https://mathworld.wolfram.com/WeibullDistribution.html
#
setMethod("skewness", signature(x = "Beta"),
function(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...){
dots <- match.call(call = sys.call(sys.parent(1)),
expand.dots = FALSE)$"..."
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))||(!isTRUE(all.equal(ncp(x),0))))
return(skewness(as(x,"AbscontDistribution"),...))
else
{a<-shape1(x); b<- shape2(x)
ret.v <- 2*(b-a)*sqrt(a+b+1)/(a+b+2)/sqrt(a*b)
if(!propagate.names){names(ret.v) <- NULL}
return(ret.v) }
})
## source: https://mathworld.wolfram.com/BetaDistribution.html
###################################################################################
#skewness --- code P.R.:
###################################################################################
setMethod("skewness", signature(x = "Arcsine"),
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(skewness(as(x,"AbscontDistribution"),...))
else return(0)
})
Any scripts or data that you put into this service are public.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.