DPQ (version 0.5-3)

bpser: pbeta() 'bpser' series computation

Description

Compute the bpser series approximation of pbeta, the incomplete beta function. Note that when b is integer valued, the series is a sum of \(b+1\) terms.

Usage

bpser(a, b, x, log.p = FALSE, eps = 1e-15, verbose = FALSE, warn = TRUE)

Value

a list with components

r

the resulting numeric vector.

ier

an integer vector of the same length as x, providing one error code for the computation in each r[i].

Arguments

a,b

numeric and non-negative, the two shape parameters of the beta distribution.

x

numeric vector of abscissa values in \([0,1]\).

log.p

a logical if log(prob) should be returned, allowing to avoid underflow much farther “out in the tails”.

eps

series convergence (and other) tolerance, a small positive number.

verbose

a logical indicating if some intermediate results should be printed to the console.

warn

a logical indicating if bpser() computation problems should be warned about in addition to return a non-zero error code.

Author

Martin Maechler, ported to DPQ; R-Core team for the code in R.

References

TOMS 708, see pbeta

See Also

pbeta.

Examples

with(bpser(100000, 11, (0:64)/64), # all 0 {last one "wrongly"}
     stopifnot(r == c(rep(0, 64), 1), err == 0))
bp1e5.11L <- bpser(100000, 11, (0:64)/64, log.p=TRUE)# -> 2 "underflow to -Inf" warnings!
pbe <- pbeta((0:64)/64, 100000, 11, log.p=TRUE)

## verbose=TRUE showing info on number of terms / iterations
ps11.5 <- bpser(100000, 11.5, (0:64)/64, log.p=TRUE, verbose=TRUE)