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 |

`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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