phyperIbeta {DPQ} | R Documentation |
Pearson's incomplete Beta function approximation to the cumulative
hyperbolic distribution function phyper(.)
.
Note that in R, pbeta()
provides a version of the
incomplete Beta function.
phyperIbeta(q, m, n, k)
q |
vector of quantiles representing the number of white balls drawn without replacement from an urn which contains both black and white balls. |
m |
the number of white balls in the urn. |
n |
the number of black balls in the urn. |
k |
the number of balls drawn from the urn, hence must be in 0,1,…, m+n. |
a numeric vector “like” q
with values approximately equal
to phyper(q,m,n,k)
.
Martin Maechler
Johnson, Kotz & Kemp (1992): (6.90), p.260 – Bol'shev (1964)
## The function is currently defined as function (q, m, n, k) { Np <- m N <- n + m n <- k x <- q p <- Np/N np <- n * p xi <- (n + Np - 1 - 2 * np)/(N - 2) d.c <- (N - n) * (1 - p) + np - 1 cc <- n * (n - 1) * p * (Np - 1)/((N - 1) * d.c) lam <- (N - 2)^2 * np * (N - n) * (1 - p)/((N - 1) * d.c * (n + Np - 1 - 2 * np)) pbeta(1 - xi, lam - x + cc, x - cc + 1) }