Description Usage Arguments Details Value Author(s) References See Also Examples
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!.
1 |
x, df, ncp |
see R's |
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
.
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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