phyperBinMolenaar {DPQ}  R Documentation 
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()
.
Usage
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)
phyperBinMolenaar (q, m, n, k, lower.tail = TRUE, log.p = FALSE) # Deprecated !
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

lower.tail 
logical; if TRUE (default), probabilities are

log.p 
logical; if TRUE, probabilities p are given as log(p). 
Details
Molenaar(1970), as cited in Johnson et al (1992), proposed
phyperBinMolenaar.1()
;
the other three are just using the mathematical symmetries of the
hyperbolic distribution, swapping k
and m
, and
using lower.tail = TRUE
or FALSE
.
Value
a numeric
vector, with the length the maximum of the
lengths of q, m, n, k
.
Author(s)
Martin Maechler
References
Johnson, N.L., Kotz, S. and Kemp, A.W. (1992)
Univariate Discrete Distributions, 2nd ed.; Wiley, doi:10.1002/bimj.4710360207.
Chapter 6, mostly Section 5 Approximations and Bounds, p.256 ff
Johnson, N.L., Kotz, S. and Kemp, A.W. (2005)
Univariate Discrete Distributions, 3rd ed.; Wiley; doi:10.1002/0471715816.
Chapter 6, Section 6.5 Approximations and Bounds, p.268 ff
See Also
phyper
, the hypergeometric distribution, and R's own
“exact” computation.
pbinom
, the binomial distribution functions.
Our utility phyperAllBin()
.
Examples
## The first function is simply
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)