The Distribution of a Positive Linear Combination of Chiqaure Random Variables
pwchisq.Rd
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 (\(\delta_1, \ldots, \delta_K\)).
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.
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))
#> [1] 0.006117973
pimeta::pwchisq(100, lambda = c(7,3), nu = c(6,2), delta = c(6,2))
#> [1] 0.5913421
pimeta::pwchisq(200, lambda = c(7,3), nu = c(6,2), delta = c(6,2))
#> [1] 0.9779184
# [1] 0.006117973
# [1] 0.5913421
# [1] 0.9779184