dhyperQ {DPQmpfr}

Exact Hypergeometric Distribution Probabilites

Description

Computes exact probabilities for the hypergeometric distribution (see, e.g., dhyper() in R), using package gmp's big integer and rational numbers, notably chooseZ().

Usage

dhyperQ(x, m, n, k)
phyperQ(x, m, n, k, lower.tail=TRUE)
phyperQall(m, n, k, lower.tail=TRUE)

Arguments

x

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 indicating if the lower or upper tail probability should be computed.

Value

a bigrational (class "bigq" from package gmp) vector “as” x; currently of length one (as all the function arguments must be “scalar”, currently).

Author(s)

Martin Maechler

See Also

chooseZ (pkg gmp), and R's own Hypergeometric

Examples

## dhyperQ() is simply
 function (x, m, n, k)
 {
    stopifnot(k - x == as.integer(k - x))
    chooseZ(m, x) * chooseZ(n, k - x) / chooseZ(m + n, k)
 }

# a case where  phyper(11, 15, 0, 12, log=TRUE) gave 'NaN'
(phyp5.0.12 <- cumsum(dhyperQ(0:12, m=15,n=0,k=12)))
stopifnot(phyp5.0.12 == c(rep(0, 12), 1))

for(x in 0:9)
  stopifnot(phyperQ(x, 10,7,8) +
            phyperQ(x, 10,7,8, lower.tail=FALSE) == 1)

(ph. <- phyperQall(m=10, n=7, k=8))
## Big Rational ('bigq') object of length 8:
## [1] 1/2431    5/374     569/4862  2039/4862 3803/4862 4685/4862 4853/4862 1
stopifnot(identical(gmp::c_bigq(list(0, ph.)),
                    1- c(phyperQall(10,7,8, lower.tail=FALSE), 0)))

(doExtras <- DPQmpfr:::doExtras())
if(doExtras) { # too slow for standard testing
 k <- 5000
 system.time(ph <-   phyper(k, 2*k, 2*k, 2*k)) #   0 (< 0.001 sec)
 system.time(phQ <- phyperQ(k, 2*k, 2*k, 2*k)) # 5.6 (was 6.3) sec
 ## Relative error of R's phyper()
 stopifnot(print(gmp::asNumeric(1 - ph/phQ)) < 1e-14) # seen 1.063e-15
}