qpoisR {DPQ}

Pure R Implementation of R's qpois() with Tuning Parameters

Description

A pure R implementation, including many tuning parameter arguments, of R's own Rmathlib C code algorithm, but with more flexibility.

It is using Vectorize(qpoisR1, *) where the hidden qpoisR1 works for numbers (aka ‘scalar’, length one) arguments only, the same as the C code.

Usage

qpoisR(p, lambda, lower.tail = TRUE, log.p = FALSE,
       yLarge = 4096, # was hard wired to 1e5
       incF = 1/64,   # was hard wired to .001
       iShrink = 8,   # was hard wired to 100
       relTol = 1e-15,# was hard wired to 1e-15
       pfEps.n = 8,   # was hard wired to 64: "fuzz to ensure left continuity"
       pfEps.L = 2,   # was hard wired to 64:   "   "   ..
       fpf = 4, # *MUST* be >= 1 (did not exist previously)
       trace = 0)

Arguments

p, lambda, lower.tail, log.p

qpois() standard argument, see its help page.

yLarge

a positive number; in R up to 2021, was internally hardwired to yLarge = 1e5: Uses more careful search for y \ge y_L, where y is the initial approximate result, derived from a Cornish-Fisher expansiion.

incF

a positive “increment factor” (originally hardwired to 0.001), used only when y >= yLarge; defines the initial increment in the search algorithm as incr <- floor(incF * y).

iShrink

a positive increment shrinking factor, used only when y >= yLarge to define the new increment from the old one as incr <- max(1, floor(incr/iShrink)) where the LHS was hardired original to (incr/100).

relTol

originally hard wired to 1e-15, defines the convergence tolerance for the search iterations when y >= yLarge; the iterations stop when (new) incr <= y * relTol.

pfEps.n, pfEps.L

positive factors defining “fuzz to ensure left continuity”, both originally hardwired to 64, the fuzz adjustment was

p <- p * (1 - 64 *.Machine$double.eps)

Now, pfEps.L is used if(log.p) is true and pfEps.n is used otherwise ("n"ormal case), and the adjustments also depend on lower.tail, and also on fpf :

fpf

a number larger than 1, together with pfEps.n determines the fuzz-adjustment to p in the case (lower=tail=FALSE, log.p=FALSE): with e <- pfEps.n * .Machine$double.eps, the adjustment p <- p * (1 + e) is made iff 1 - p > fpf*e.

trace

logical (or integer) specifying if (and how much) output should be produced from the algorithm.

Details

The defaults and exact meaning of the algorithmic tuning arguments from yLarge to fpf were experimentally determined are subject to change.

Value

a numeric vector like p recycled to the common lengths of p and lambda.

Author(s)

Martin Maechler

See Also

qpois.

Examples

x <- 10*(15:25)
Pp <- ppois(x, lambda = 100, lower.tail = FALSE)  # no cancellation
qPp <- qpois(Pp, lambda = 100, lower.tail=FALSE)
table(x == qPp) # all TRUE ?
## future: if(getRversion() >= "4.2") stopifnot(x == qPp) # R-devel
qpRp <- qpoisR(Pp, lambda = 100, lower.tail=FALSE)
all.equal(x, qpRp, tol = 0)
stopifnot(all.equal(x, qpRp, tol = 1e-15))