2.16.4 cdfchn: ----- cumulative distribution function non-central chi-square distribution
CALLING SEQUENCE
[P,Q]=cdfchn("PQ",X,Df,Pnonc)
[X]=cdfchn("X",Df,Pnonc,P,Q);
[Df]=cdfchn("Df",Pnonc,P,Q,X)
[Pnonc]=cdfchn("Pnonc",P,Q,X,Df)
PARAMETERS
-
P,Q,X,Df,Pnonc
: five real vectors of the same size.
- P,Q (Q=1-P)
: The integral from 0 to X of the non-central chi-square
distribution.
Input range: [0, 1-1E-16).
- X
: Upper limit of integration of the non-central chi-square distribution.
Input range: [0, +infinity).
Search range: [0,1E300]
- Df
: Degrees of freedom of the non-central
chi-square distribution.
Input range: (0, +infinity).
Search range: [ 1E-300, 1E300]
- Pnonc
: Non-centrality parameter of the non-central
chi-square distribution.
Input range: [0, +infinity).
Search range: [0,1E4]
DESCRIPTION
Calculates any one parameter of the non-central chi-square
distribution given values for the others.
Formula 26.4.25 of Abramowitz and Stegun, Handbook of
Mathematical Functions (1966) is used to compute the cumulative
distribution function.
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.
The computation time required for this routine is proportional
to the noncentrality parameter (PNONC). Very large values of
this parameter can consume immense computer resources. This is
why the search range is bounded by 10,000.
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.