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# Copyright 2014-2015 Steven E. Pav. All Rights Reserved.
# Author: Steven E. Pav
#
# This file is part of sadists.
#
# sadists is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# sadists is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with sadists. If not, see <http://www.gnu.org/licenses/>.
# Created: 2015.02.08
# Copyright: Steven E. Pav, 2015
# Author: Steven E. Pav
# Comments: Steven E. Pav
# we need a vectorized confluent hypergeometric function#FOLDUP
F11 <- Vectorize(hypergeo::genhypergeo,vectorize.args=c("U","L","z"))
ReF11 <- function(...) {
return(Re(F11(...)))
}
#UNFOLD
# some moments of standard distributions:#FOLDUP
# compute the 1 through order.max raw, uncentered moment
# of the normal distribution with given mean and standard
# deviation
norm_moms <- function(mu=0,sigma=1,order.max=3) {
retval <- rep(1,order.max)
hermi <- orthopolynom::hermite.he.polynomials(order.max, normalized=FALSE)
for (iii in c(1:order.max)) {
cvals <- abs(coefficients(hermi[[iii+1]]))
lvals <- mu^(0:iii) * sigma^(iii - (0:iii))
retval[iii] <- sum(cvals * lvals)
}
return(retval)
}
# compute the 1 through order.max raw, uncentered moment
# of the (non-central) chisquare to power distribution.
chipow_moms <- function(df,ncp=0,pow=1,order.max=3,orders=1:order.max,log=FALSE) {
retval <- chisq_moms(df=df,ncp=ncp,orders=pow * orders,log=log)
return(retval)
}
# compute the 1 through order.max raw, uncentered moment
# of the (non-central) chi-square distribution with df d.f.
# c.f. Paolella 10.9
chisq_moms <- function(df,ncp=0,order.max=3,orders=1:order.max,log=FALSE) {
hadf <- df/2.0
hancp <- ncp/2.0
if (log) {
retval <- orders * log(2.0) + lgamrat(orders + hadf,hadf)
if (ncp != 0) {
retval <- retval - hancp + log(ReF11(orders + hadf,hadf,hancp))
}
} else {
retval <- (2.0^(orders)) * gamrat(orders + hadf,hadf)
if (ncp != 0) {
retval <- (retval/exp(hancp)) * ReF11(orders + hadf,hadf,hancp)
}
}
return(retval)
}
#UNFOLD
#for vim modeline: (do not edit)
# vim:fdm=marker:fmr=FOLDUP,UNFOLD:cms=#%s:syn=r:ft=r
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