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# 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)```

• cdfbet — cumulative distribution function Beta distribution
• cdfbin — cumulative distribution function Binomial distribution
• cdfchi — cumulative distribution function chi-square distribution
• cdfchn — cumulative distribution function non-central chi-square distribution
• cdffnc — cumulative distribution function non-central f-distribution
• cdfgam — cumulative distribution function gamma distribution
• cdfnbn — cumulative distribution function negative binomial distribution
• cdfnor — cumulative distribution function normal distribution
• cdfpoi — cumulative distribution function poisson distribution
• cdft — cumulative distribution function Student's T distribution
 Report an issue << cdfchn Cumulated Distribution Functions cdffnc >>

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