cdff
====

cumulative distribution function F distribution



Calling Sequence
~~~~~~~~~~~~~~~~


::

    [P,Q]=cdff("PQ",F,Dfn,Dfd)
    [F]=cdff("F",Dfn,Dfd,P,Q);
    [Dfn]=cdff("Dfn",Dfd,P,Q,F);
    [Dfd]=cdff("Dfd",P,Q,F,Dfn)




Arguments
~~~~~~~~~

:P,Q,F,Dfn,Dfd five real vectors of the same size.
: :P,Q (Q=1-P) The integral from 0 to F of the f-density. Input range:
  [0,1].
: :F Upper limit of integration of the 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. Input
  range: (0, +infinity). Search range: [ 1E-300, 1E300]
:



Description
~~~~~~~~~~~

Calculates any one parameter of the F distribution given values for
the others.

Formula 26.6.2 of Abramowitz and Stegun, Handbook of Mathematical
Functions (1966) is used to reduce the computation of the cumulative
distribution function for the F variate to that of an incomplete beta.

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 value of the cumulative 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.