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!.
the number of terms to be used, a positive integer.
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).
mpfr vector of the same length as the maximum
of the lengths of
x, df, ncp.
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
1 2 3 4 5 6 7 8 9 10
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
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