sadists (version 0.2.5)

sumlogchisq: The sum of the logs of (non-central) chi-squares distribution.

Description

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

Usage

dsumlogchisq(x, wts, df, ncp=0, log = FALSE, order.max=6)
psumlogchisq(q, wts, df, ncp=0, lower.tail = TRUE, log.p = FALSE, order.max=6)
qsumlogchisq(p, wts, df, ncp=0, lower.tail = TRUE, log.p = FALSE, order.max=6)
rsumlogchisq(n, wts, df, ncp=0)

Value

dsumlogchisq gives the density, psumlogchisq gives the distribution function, qsumlogchisq gives the quantile function, and rsumlogchisq 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, but not against the x,q,p,n.

df

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

ncp

the vector of non-centrality parameters. This is recycled against the wts, df, 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 \(w_i\) be given constants. Suppose $$Y = \sum_i w_i \log X_i.$$ Then \(Y\) follows a weighted sum of log of chi-squares distribution.

References

Pav, Steven. Moments of the log non-central chi-square distribution. https://arxiv.org/abs/1503.06266

See Also

The product of chi-squares to a power, dprodchisqpow, pprodchisqpow, qprodchisqpow, rprodchisqpow.

Examples

wts <- c(1,-3,4)
df <- c(100,20,10)
ncp <- c(5,3,1)
rvs <- rsumlogchisq(128, wts, df, ncp)
dvs <- dsumlogchisq(rvs, wts, df, ncp)
qvs <- psumlogchisq(rvs, wts, df, ncp)
pvs <- qsumlogchisq(ppoints(length(rvs)), wts, df, ncp)