# cdfchn

cumulative distribution function non-central chi-square distribution

## Calling Sequence

    [P,Q]=cdfchn("PQ",X,Df,Pnonc)
                [X]=cdfchn("X",Df,Pnonc,P,Q);
                [Df]=cdfchn("Df",Pnonc,P,Q,X)
                [Pnonc]=cdfchn("Pnonc",P,Q,X,Df)

## Arguments

P,Q,X,Df,Pnonc

  five real vectors of the same size.

P,Q (Q=1-P)

  The integral from 0 to X of the non-central chi-square distribution. Input range: [0, 1-1E-16).

X

  Upper limit of integration of the non-central chi-square distribution. Input range: [0, +infinity). Search range: [0,1E300]

Df

  Degrees of freedom of the non-central chi-square distribution. Input range: (0, +infinity). Search range: [ 1E-300, 1E300]

Pnonc

  Non-centrality parameter of the non-central chi-square distribution. Input range: [0, +infinity). Search range: [0,1E4]

## Description

Calculates any one parameter of the non-central chi-square distribution given values for the others.

Formula 26.4.25 of Abramowitz and Stegun, Handbook of Mathematical Functions (1966) is used to compute the cumulative distribution function.

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 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.

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 `x=0.1` for the non-central chi-square distribution function with `Df=2` and `Pnonc=5`.

        Pnonc = 5;
        Df = 2;
        x = 0.1;
        // Expected : P = 0.0042567 and Q = 1-P
        [P, Q] = cdfchn("PQ", x, Df, Pnonc)

## See Also

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