dnt {DPQmpfr}

Non-central t-Distribution Density

Description

dntJKBm is a fully Rmpfr-ified vectorized version of dntJKBf() from DPQ which implements the summation formulas of Johnson, Kotz and Balakrishnan (1995), (31.15) on page 516 and (31.15') on p.519, the latter being typo-corrected for a missing factor 1 / j!.

Usage

dntJKBm(x, df, ncp, log = FALSE, M = 1000)

Arguments

x, df, ncp

see R's dt(); note that each can be of class "mpfr".

log

as in dt(), a logical indicating if \log(f(x,*)) should be returned instead of f(x,*).

M

the number of terms to be used, a positive integer.

Details

How to choose M optimally has not been investigated yet and is probably also a function of the precision of the first three arguments (see getPrec from Rmpfr).

Value

an mpfr vector of the same length as the maximum of the lengths of x, df, ncp.

Author(s)

Martin Maechler

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

dt.

Examples

require(Rmpfr)
## [not too large, as dntJKBm() is currently somewhat slow]
(mt  <- mpfr(tt  <- seq(0, 9, by =  1 ), 128))
(mcp <- mpfr(ncp <- seq(0, 5, by = 1/2), 128))
dt3R <- outer(tt, ncp, dt,   df = 3)
dt3M <- outer(mt, mcp, dntJKBm, df = 3, M = 128)# for speed
all.equal(dt3R, dt3M) # TRUE, and show difference
all.equal(dt3R, dt3M, tol=0) # 1.2e-12