dnt {DPQmpfr} | R Documentation |
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!.
dntJKBm(x, df, ncp, log = FALSE, M = 1000)
x, df, ncp |
|
log |
as in |
M |
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).
an mpfr
vector of the same length as the maximum
of the lengths of x, df, ncp
.
Martin Maechler
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
dt
.
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