pnt

0th

Percentile

Non-central t Probability Distribution - Algorithms and Approximations

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

Keywords
distribution, math
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.

Details

.:

..

.:

..

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().

.:

..

.:

..

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().

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.

Aliases
  • pntR
  • pntR1
  • pntP94
  • pntP94.1
  • pntLrg
  • pntJW39
  • pntJW39.0
  • pntChShP94
  • pntChShP94.1
  • pnt3150
  • pnt3150.1
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
# }
Documentation reproduced from package DPQ, version 0.3-3, License: GPL (>= 2)

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