pwchisq: The Distribution of a Positive Linear Combination of Chiqaure...

In nshi-stat/pimeta: Prediction Intervals for Random-Effects Meta-Analysis

The Distribution of a Positive Linear Combination of Chiqaure Random Variables

Description

The cumulative distribution function for the distribution of a positive linear combination of \chi^2 random variables with the weights (\lambda_1, \ldots, \lambda_K), degrees of freedom (\nu_1, \ldots, \nu_K), and non-centrality parameters (\delta_1, \ldots, \delta_K).

Usage

pwchisq(
  x,
  lambda = 1,
  nu = 1,
  delta = 0,
  mode = 1,
  maxit1 = 1e+05,
  eps = 10^(-10)
)

Arguments

x	numeric; value of x > 0 (P[X \le x]).
lambda	numeric vector; weights (\lambda_1, \ldots, \lambda_K).
nu	integer vector; degrees of freedom (\nu_1, \ldots, \nu_K).
delta	numeric vector; non-centrality parameters (\delta_1, \ldots, \delta_K).
mode	numeric; the mode of calculation (see Farabrother, 1984)
maxit1	integer; the maximum number of iteration.
eps	numeric; the desired level of accuracy.

Value

• prob: the distribution function.

References

Farebrother, R. W. (1984). Algorithm AS 204: the distribution of a positive linear combination of \chi^2 random variables. J R Stat Soc Ser C Appl Stat. 33(3): 332–339. https://rss.onlinelibrary.wiley.com/doi/10.2307/2347721.

Examples

# Table 1 of Farabrother (1984)
# Q6 (The taget values are 0.0061, 0.5913, and 0.9779)

pimeta::pwchisq( 20, lambda = c(7,3), nu = c(6,2), delta = c(6,2))
pimeta::pwchisq(100, lambda = c(7,3), nu = c(6,2), delta = c(6,2))
pimeta::pwchisq(200, lambda = c(7,3), nu = c(6,2), delta = c(6,2))
# [1] 0.006117973
# [1] 0.5913421
# [1] 0.9779184

nshi-stat/pimeta documentation built on June 8, 2025, 10:23 p.m.