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.TH cdfnbn 1 "Dec 1997" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
cdfnbn - cumulative distribution function negative binomial distribution
.SH CALLING SEQUENCE
.nf
[P,Q]=cdfnbn("PQ",S,Xn,Pr,Ompr)
[S]=cdfnbn("S",Xn,Pr,Ompr,P,Q)
[Xn]=cdfnbn("Xn",Pr,Ompr,P,Q,S)
[Pr,Ompr]=cdfnbn("PrOmpr",P,Q,S,Xn)
.fi
.SH PARAMETERS
.TP 10
P,Q,S,Xn,Pr,Ompr
: six real vectors of the same size.
.TP
P,Q (Q=1-P)
: The cumulation from 0 to S of the negative
binomial distribution.
Input range: [0,1].
.TP
S
: The upper limit of cumulation of the binomial distribution.
There are F or fewer failures before the XNth success.
Input range: [0, +infinity).
Search range: [0, 1E300]
.TP
Xn
: The number of successes.
Input range: [0, +infinity).
Search range: [0, 1E300]
.TP
Pr
: The probability of success in each binomial trial.
Input range: [0,1].
Search range: [0,1].
.TP
Ompr
: 1-PR
Input range: [0,1].
Search range: [0,1]
PR + OMPR = 1.0
.SH DESCRIPTION
Calculates any one parameter of the negative binomial
distribution given values for the others.
.LP
The cumulative negative binomial distribution returns the
probability that there will be F or fewer failures before the
XNth success in binomial trials each of which has probability of
success PR.
.LP
The individual term of the negative binomial is the probability of
S failures before XN successes and is
Choose( S, XN+S-1 ) * PR^(XN) * (1-PR)^S
.LP
Formula 26.5.26 of Abramowitz and Stegun, Handbook of
Mathematical Functions (1966) is used to reduce calculation of
the cumulative distribution function to that of an incomplete
beta.
.LP
Computation of other parameters involve a seach for a value that
produces the desired value of P. The search relies on the
monotinicity of P with the other parameter.
.LP
From DCDFLIB: Library of Fortran Routines for Cumulative Distribution
Functions, Inverses, and Other Parameters (February, 1994)
Barry W. Brown, James Lovato and Kathy Russell. The University of
Texas.
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