# cdff

cumulative distribution function Fisher 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 search for a value that produces the desired value of P. The search relies on the monotonicity 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.

In certain cases, the degrees of freedom are not integers. Scilab then issues a warning.

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.

## Examples

In the following example, we compute the probability of the event `f=0.1` for the Fisher distribution function with `Dfn=2` and `Dfd=2`.

        Dfn = 2;
        Dfd = 2;
        f = 0.1;
        // Expected : P = 0.0909091 and Q = 1-P
        [P, Q] = cdff("PQ", f, Dfd, Dfd)

## See Also

- cdfbet
- cdfbin
- cdfchi
- cdfchn
- cdffnc
- cdfgam
- cdfnbn
- cdfnor
- cdfpoi
- cdft