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cdffnc(1) Scilab Function cdffnc(1)
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 Mathemati-
cal Functions (1966) is used to compute the cumulative distribution func-
tion.
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 neces-
sarily 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 Func-
tions, Inverses, and Other Parameters (February, 1994) Barry W. Brown,
James Lovato and Kathy Russell. The University of Texas.
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