cdff

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 — 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