#### Documented in dprodchisqpowpprodchisqpowqprodchisqpowrprodchisqpow

# 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
# 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

#
# Created: 2015.03.07
# Copyright: Steven E. Pav, 2015
# Author: Steven E. Pav

# dprodchisqpow, pprodchisqpow, qprodchisqpow, rprodchisqpow#FOLDUP
#' @title The product of (non-central) chi-squares raised to powers distribution.
#'
#' @description
#'
#' Density, distribution function, quantile function and random
#' generation for the distribution of the product of non-central
#' chi-squares taken to powers.
#'
#' @details
#'
#' Let \eqn{X_i \sim \chi^2\left(\delta_i, \nu_i\right)}{X_i ~ chi^2(delta_i, v_i)}
#' be independently distributed non-central chi-squares, where \eqn{\nu_i}{v_i}
#' are the degrees of freedom, and \eqn{\delta_i}{delta_i} are the
#' non-centrality parameters.
#' Let \eqn{p_i} be given constants. Suppose
#' \deqn{Y = \prod_i X_i^{p_i}.}{Y = prod w_i (X_i)^(p_i).}
#' Then \eqn{Y}{Y} follows a product of chi-squares to power distribution.
#'
#' @usage
#'
#' dprodchisqpow(x, df, ncp=0, pow=1, log = FALSE, order.max=5)
#'
#' pprodchisqpow(q, df, ncp=0, pow=1, lower.tail = TRUE, log.p = FALSE, order.max=5)
#'
#' qprodchisqpow(p, df, ncp=0, pow=1, lower.tail = TRUE, log.p = FALSE, order.max=5)
#'
#' rprodchisqpow(n, df, ncp=0, pow=1)
#'
#' @param x,q vector of quantiles.
#' @param p vector of probabilities.
#' @param n number of observations.
#' @param df the vector of degrees of freedom.
#' This is recycled against the \code{ncp, pow}, but not against the \code{x,q,p,n}.
#' @param ncp the vector of non-centrality parameters.
#' This is recycled against the \code{df, pow}, but not against the \code{x,q,p,n}.
#' @param pow the vector of the power parameters.
#' This is recycled against the \code{df, ncp}, but not against the \code{x,q,p,n}.
#'
#' @template etc
#' @template distribution
#' @template apx_distribution
#' @template not-recycled
#' @template ref-lnc
#' @note The PDQ functions are computed by translation of the
#' sum of log chi-squares distribution functions.
#'
#' @return \code{dprodchisqpow} gives the density, \code{pprodchisqpow} gives the
#' distribution function, \code{qprodchisqpow} gives the quantile function,
#' and \code{rprodchisqpow} generates random deviates.
#'
#' Invalid arguments will result in return value \code{NaN} with a warning.
#' @aliases dprodchisqpow pprodchisqpow qprodchisqpow rprodchisqpow
#' @seealso
#' The sum of log of chi-squares distribution,
#' The upsilon distribution,
#' The sum of chi-square powers distribution,
#' @examples
#' df <- c(100,20,10)
#' ncp <- c(5,3,1)
#' pow <- c(1,0.5,1)
#' rvs <- rprodchisqpow(128, df, ncp, pow)
#' dvs <- dprodchisqpow(rvs, df, ncp, pow)
#' qvs <- pprodchisqpow(rvs, df, ncp, pow)
#' pvs <- qprodchisqpow(ppoints(length(rvs)), df, ncp, pow)
#' @rdname dprodchisqpow
#' @name prodchisqpow
#' @export
dprodchisqpow <- function(x, df, ncp=0, pow=1, log = FALSE, order.max=5) {
retval <- dsumlogchisq(x=log(x),wts=pow,df=df,ncp=ncp,log=log,order.max=order.max)
if (log) {
retval <- retval - log(x)
} else {
retval <- retval/x
}
return(retval)
}
#' @export
pprodchisqpow <- function(q, df, ncp=0, pow=1, lower.tail = TRUE, log.p = FALSE, order.max=5) {
retval <- psumlogchisq(log(q),wts=pow,df=df,ncp=ncp,lower.tail=lower.tail,log.p=log.p,order.max=order.max)
return(retval)
}
#' @export
qprodchisqpow <- function(p, df, ncp=0, pow=1, lower.tail = TRUE, log.p = FALSE, order.max=5) {
retval <- qsumlogchisq(p,wts=pow,df=df,ncp=ncp,lower.tail=lower.tail,log.p=log.p,order.max=order.max)
retval <- exp(retval)
return(retval)
}
#' @export
rprodchisqpow <- function(n, df, ncp=0, pow=1) {
subX <- mapply(function(dd,nn,pp) { (unbroken_rchisq(n,df=dd,ncp=nn) ^ pp) },
df,ncp,pow,SIMPLIFY=FALSE)
X <- Reduce('*', subX)
return(X)
}
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shabbychef/sadists documentation built on May 29, 2019, 8:06 p.m.