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cdffnc Scilab Group Scilab Function cdffnc
NAME
cdffnc - cumulative distribution function non-central f-distribution
CALLING SEQUENCE
[P,Q]=cdffnc("PQ",F,Dfn,Dfd,Pnonc)
[F]=cdffnc("F",Dfn,Dfd,Pnonc,P,Q);
[Dfn]=cdffnc("Dfn",Dfd,Pnonc,P,Q,F);
[Dfd]=cdffnc("Dfd",Pnonc,P,Q,F,Dfn)
[Pnonc]=cdffnc("Pnonc",P,Q,F,Dfn,Dfd);
PARAMETERS
P,Q,F,Dfn,Dfd,Pnonc
: six real vectors of the same size.
P,Q (Q=1-P)
The integral from 0 to F of the non-central f-density. Input range:
[0,1-1E-16).
F : Upper limit of integration of the non-central f-density.
Input range: [0, +infinity). Search range: [0,1E300]
Dfn : Degrees of freedom of the numerator sum of squares. Input
range: (0, +infinity). Search range: [ 1E-300, 1E300]
Dfd : Degrees of freedom of the denominator sum of squares. Must
be in range: (0, +infinity). Input range: (0, +infinity).
Search range: [ 1E-300, 1E300]
Pnonc : The non-centrality parameter Input range: [0,infinity)
Search range: [0,1E4]
DESCRIPTION
Calculates any one parameter of the Non-central F distribution given
values for the others.
Formula 26.6.20 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.
The value of the cumulative noncentral F distribution is not
necessarily monotone in either degrees of freedom. There thus may be
two values that provide a given CDF value. This routine assumes
monotonicity and will find an arbitrary one of the two values.
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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