phyperAllBin {DPQ}

Compute Hypergeometric Probabilities via Binomial Approximations

Description

Simple utilities for ease of comparison of the different phyper approximation in package DPQ:

• phyperAllBinM() computes all four Molenaar binomial approximations to the hypergeometric cumulative distribution function phyper().

• phyperAllBin() computes Molenaar's four and additionally the other four phyperBin.1(), *.2, *.3, and *.4.

• .suppHyper(), support of the Hyperbolic, is a simple 1-liner, providing all sensible integer values for the first argument q (or also x) of the hyperbolic probability functions (dhyper() and phyper()), and their approximations (here in DPQ).

Usage

phyperAllBin (m, n, k, q = .suppHyper(m, n, k), lower.tail = TRUE, log.p = FALSE)
phyperAllBinM(m, n, k, q = .suppHyper(m, n, k), lower.tail = TRUE, log.p = FALSE)
.suppHyper(m, n, k)

Arguments

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.

q

vector of quantiles representing the number of white balls drawn without replacement from an urn which contains both black and white balls. The default, .suppHyper(m, n, k) provides the full (finite) support.

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).

Value

the phyperAllBin*() functions return a numeric matrix, with each column a different approximation to phyper(m,n,k,q, lower.tail, log.p).

Note that the columns of phyperAllBinM() are a subset of those from phyperAllBin().

Author(s)

Martin Maechler

References

See those in phyperBinMolenaar.

See Also

phyperBin.1 etc, and phyperBinMolenaar.

phyper

Examples

.suppHyper # very simple:
stopifnot(identical(.suppHyper, ignore.environment = TRUE,
         function (m, n, k) max(0, k-n):min(k, m)))

phBall <- phyperAllBin (5,15, 7)
phBalM <- phyperAllBinM(5,15, 7)
stopifnot(identical( ## indeed, ph...AllBinM() gives a *subset* of ph...AllBin():
            phBall[, colnames(phBalM)] ,
            phBalM)
         , .suppHyper(5, 15, 7) == 0:5
)

round(phBall, 4)
cbind(q = 0:5, round(-log10(abs(1 - phBall / phyper(0:5, 5,15,7))),  digits=2))

require(sfsmisc)## -->  relErrV() {and eaxis()}: 
qq <-    .suppHyper(20, 47, 31)
phA <- phyperAllBin(20, 47, 31)
rE <- relErrV(target = phyper(qq, 20,47,31), phA)
signif(cbind(qq, rE), 4)
## Relative approximation error [ log scaled ] :
matplot(qq, abs(rE), type="b", log="y", yaxt="n")
eaxis(2)
## ---> approximations useful only "on the right", aka the right tail