sadists (version 0.2.5)

sumchisqpow: The sum of (non-central) chi-squares raised to powers distribution.

Description

Density, distribution function, quantile function and random generation for the distribution of the weighted sum of non-central chi-squares taken to powers.

Usage

dsumchisqpow(x, wts, df, ncp=0, pow=1, log = FALSE, order.max=6)
psumchisqpow(q, wts, df, ncp=0, pow=1, lower.tail = TRUE, log.p = FALSE, order.max=6)
qsumchisqpow(p, wts, df, ncp=0, pow=1, lower.tail = TRUE, log.p = FALSE, order.max=6)
rsumchisqpow(n, wts, df, ncp=0, pow=1)

Value

dsumchisqpow gives the density, psumchisqpow gives the distribution function, qsumchisqpow gives the quantile function, and rsumchisqpow generates random deviates.

Invalid arguments will result in return value NaN with a warning.

Arguments

x, q

vector of quantiles.

wts

the vector of weights. This is recycled against the df, ncp, pow, but not against the x,q,p,n.

df

the vector of degrees of freedom. This is recycled against the wts, ncp, pow, but not against the x,q,p,n.

ncp

the vector of non-centrality parameters. This is recycled against the wts, df, pow, but not against the x,q,p,n.

pow

the vector of the power parameters. This is recycled against the wts, df, ncp, but not against the x,q,p,n.

log

logical; if TRUE, densities \(f\) are given as \(\mbox{log}(f)\).

order.max

the order to use in the approximate density, distribution, and quantile computations, via the Gram-Charlier, Edeworth, or Cornish-Fisher expansion.

p

vector of probabilities.

n

number of observations.

log.p

logical; if TRUE, probabilities p are given as \(\mbox{log}(p)\).

lower.tail

logical; if TRUE (default), probabilities are \(P[X \le x]\), otherwise, \(P[X > x]\).

Author

Steven E. Pav

Details

Let \(X_i \sim \chi^2\left(\delta_i, \nu_i\right)\) be independently distributed non-central chi-squares, where \(\nu_i\) are the degrees of freedom, and \(\delta_i\) are the non-centrality parameters. Let \(w_i\) and \(p_i\) be given constants. Suppose $$Y = \sum_i w_i X_i^{p_i}.$$ Then \(Y\) follows a weighted sum of chi-squares to power distribution.

See Also

The upsilon distribution, dupsilon,pupsilon,qupsilon,rupsilon.

Examples

wts <- c(1,-3,4)
df <- c(100,20,10)
ncp <- c(5,3,1)
pow <- c(1,0.5,1)
rvs <- rsumchisqpow(128, wts, df, ncp, pow)
dvs <- dsumchisqpow(rvs, wts, df, ncp, pow)
qvs <- psumchisqpow(rvs, wts, df, ncp, pow)
pvs <- qsumchisqpow(ppoints(length(rvs)), wts, df, ncp, pow)