DPQ (version 0.3-3)

pnt: Non-central t Probability Distribution - Algorithms and Approximations

Description

Compute different approximations for the non-central t-Distribution cumulative probability distribution function.

Usage

pntR      (t, df, ncp, lower.tail = TRUE, log.p = FALSE,
                                          itrmax = 1000, errmax = 1e-12, verbose = TRUE)
pntR1     (t, df, ncp, lower.tail = TRUE, log.p = FALSE,
                                          itrmax = 1000, errmax = 1e-12, verbose = TRUE)
pnt3150   (t, df, ncp, lower.tail = TRUE, log.p = FALSE, M = 1000, verbose = TRUE)
pnt3150.1 (t, df, ncp, lower.tail = TRUE, log.p = FALSE, M = 1000, verbose = TRUE)
pntP94    (t, df, ncp, lower.tail = TRUE, log.p = FALSE,
                                          itrmax = 1000, errmax = 1e-12, verbose = TRUE)
pntP94.1  (t, df, ncp, lower.tail = TRUE, log.p = FALSE,
                                          itrmax = 1000, errmax = 1e-12, verbose = TRUE)
pntLrg    (t, df, ncp, lower.tail = TRUE, log.p = FALSE)
pntJW39   (t, df, ncp, lower.tail = TRUE, log.p = FALSE)
pntJW39.0 (t, df, ncp, lower.tail = TRUE, log.p = FALSE)
pntChShP94  (t, df, ncp, lower.tail = TRUE, log.p = FALSE,
                                            itrmax = 1000, errmax = 1e-12, verbose = TRUE)
pntChShP94.1(t, df, ncp, lower.tail = TRUE, log.p = FALSE,
                                            itrmax = 1000, errmax = 1e-12, verbose = TRUE)

Arguments

t

vector of quantiles (called q in pt(..).

df

degrees of freedom (\(> 0\), maybe non-integer). df = Inf is allowed.

ncp

non-centrality parameter \(\delta\); currently except for rt(), only for abs(ncp) <= 37.62. If omitted, use the central t distribution.

log, log.p

logical; if TRUE, probabilities p are given as log(p).

lower.tail

logical; if TRUE (default), probabilities are \(P[X \le x]\), otherwise, \(P[X > x]\).

itrmax

...

errmax

...

verbose

...

M

positive integer specifying the number of terms to use in the series.

Value

a number for pntJKBf1() and .pntJKBch1().

a numeric vector of the same length as the maximum of the lengths of x, df, ncp for pntJKBf() and .pntJKBch().

Details

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..

.:

..

pnt3150(), pnt3150.1():

Simple inefficient but hopefully correct version of pntP94..() This is really a direct implementation of formula (31.50), p.532 of Johnson, Kotz and Balakrishnan (1995)

pntP94(), pntP94.1():

New versions of pntR1(), pntR(); using the Posten (1994) algorithm. pntP94() is the Vectorize()d version of pntP94.1().

.:

..

.:

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References

Johnson, N.L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions Vol~2, 2nd ed.; Wiley. Chapter 31, Section 5 Distribution Function, p.514 ff

See Also

pt, for R's version of non-central t probabilities.

Examples

# NOT RUN {
tt <- seq(0, 10, len = 21)
ncp <- seq(0, 6, len = 31)
dt3R   <- outer(tt, ncp, pt, , df = 3)
dt3JKB <- outer(tt, ncp, pntR, df = 3)# currently verbose
stopifnot(all.equal(dt3R, dt3JKB, tolerance = 4e-15))# 64-bit Lnx: 2.78e-16
# }