Scilab Function
Last update : Dec 1997

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 Mathematical Functions (1966) is used to compute the cumulative distribution function.

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 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.