pwchisq function

The Distribution of a Positive Linear Combination of Chiqaure Random Variables

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 ($\delta_1, \ldots, \delta_K$).

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.

Returns

• prob: the distribution function.

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

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.