phyperR2 {DPQ}

Pure R version of R's C level phyper()

Description

Use pure R functions to compute (less efficiently and usually even less accurately) hypergeometric (point) probabilities with the same "Welinder"-algorithm as R's C level code has been doing since 2004.

Apart from boundary cases, each phyperR2() call uses one corresponding pdhyper() call.

Usage

phyperR2(q, m, n, k, lower.tail = TRUE, log.p = FALSE, ...)
pdhyper (q, m, n, k,                    log.p = FALSE,
         epsC = .Machine$double.eps, verbose = getOption("verbose"))

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).

...

further arguments, passed to pdhyper().

epsC

a non-negative number, the computer epsilon to be used; effectively a relative convergence tolerance for the while() loop in pdhyper().

verbose

logical indicating if the pdhyper() calls, typically one per phyperR2() call, should show how many terms have been computed and summed up.

Value

a number (as q).

pdhyper(q, m,n,k)

computes the ratio phyper(q, m,n,k) / dhyper(q, m,n,k) but without computing numerator or denominator explicitly.

phyperR2()

(in the non-boundary cases) then just computes the product dhyper(..) * pdhyper(..), of course “modulo” lower.tail and log.p transformations.

Consequently, it typically returns values very close to the corresponding R phyper(q, m,n,k, ..) call.

Note

For now, all arguments of these functions must be of length one.

Author(s)

Martin Maechler, based on R's C code originally provided by Morton Welinder from the Gnumeric project, who thanks Ian Smith for ideas.

References

Morten Welinder (2004) phyper accuracy and efficiency; R bug report PR#6772; https://bugs.r-project.org/show_bug.cgi?id=6772

See Also

phyper

Examples

## same example as phyper()
m <- 10; n <- 7; k <- 8
vapply(0:9, phyperR2, 0.1, m=m, n=n, k=k)  ==  phyper(0:9, m,n,k)
##  *all* TRUE (for 64b FC30)

## 'verbose=TRUE' to see the number of terms used:
vapply(0:9, phyperR2, 0.1, m=m, n=n, k=k,  verbose=TRUE)

## Larger arguments:
k <- 100 ; x <- .suppHyper(k,k,k)
ph  <- phyper (x, k,k,k)
ph1 <- phyperR(x, k,k,k) # ~ old R version
ph2 <- vapply(x, phyperR2, 0.1, m=k, n=k, k=k)
cbind(x, ph, ph1, ph2, rE1 = 1-ph1/ph, rE = 1-ph2/ph)
stopifnot(abs(1 -ph2/ph) < 8e-16) # 64bit FC30: see -2.22e-16 <= rE <= 3.33e-16

## Morten Welinder's example:
(p1R <- phyperR (59, 150, 150, 60, lower.tail=FALSE))
## gave 6.372680161e-14 in "old R";, here -1.04361e-14 (worse!!)
(p1x <-  dhyper ( 0, 150, 150, 60))# is 5.111204798e-22.
(p1N <- phyperR2(59, 150, 150, 60, lower.tail=FALSE)) # .. "perfect"
(p1. <- phyper  (59, 150, 150, 60, lower.tail=FALSE))# R's own
all.equal(p1x, p1N, tol=0) # on Lnx even perfectly
all.equal(p1x, p1., tol=0) # on Lnx even perfectly