DPQ (version 0.5-3)

phyperBinMolenaar: HyperGeometric Distribution via Molenaar's Binomial Approximation

Description

Compute hypergeometric cumulative probabilities via Molenaar's binomial approximations. The arguments of these functions are exactly those of R's own phyper().

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Usage

phyperBinMolenaar  (q, m, n, k, lower.tail = TRUE, log.p = FALSE)
phyperBinMolenaar.1(q, m, n, k, lower.tail = TRUE, log.p = FALSE)
phyperBinMolenaar.2(q, m, n, k, lower.tail = TRUE, log.p = FALSE)
phyperBinMolenaar.3(q, m, n, k, lower.tail = TRUE, log.p = FALSE)
phyperBinMolenaar.4(q, m, n, k, lower.tail = TRUE, log.p = FALSE)

Value

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Arguments

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 \(0,1,\dots, m+n\).

lower.tail

logical; if TRUE (default), probabilities are \(P[X \le x]\), otherwise, \(P[X > x]\).

log.p

logical; if TRUE, probabilities p are given as log(p).

Author

Martin Maechler

References

Johnson, N.L., Kotz, S. and Kemp, A.W. (1992) Univariate Discrete Distributions, 2nd ed.; Wiley.
Chapter 6, mostly Section 5 Approximations and Bounds, p.256 ff

See Also

phyper, the hypergeometric distribution, and R's own “exact” computation. pbinom, the binomial distribution functions.

Examples

## The function is currently defined as
function (q, m, n, k, lower.tail = TRUE, log.p = FALSE)
pbinom(q, size = k, prob = hyper2binomP(q, m, n, k), lower.tail = lower.tail,
    log.p = log.p)