# cdfchi

cumulative distribution function chi-square distribution

## Calling Sequence

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

## Arguments

P,Q,Xn,Df

  four real vectors of the same size.

P,Q (Q=1-P)

  The integral from 0 to X of the chi-square distribution. Input range: [0, 1].

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 chi-square distribution. Input range: (0, +infinity). Search range: [ 1E-300, 1E300]

## Description

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

Formula 26.4.19 of Abramowitz and Stegun, Handbook of Mathematical Functions (1966) is used to reduce the chi-square distribution to the incomplete distribution.

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.

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 chi-square distribution function with `Df=2`.

        Df = 2;
        x = 0.1;
        // Expected : P = 0.0487706 and Q = 1-P
        [P, Q] = cdfchi("PQ", x, Df)

## See Also

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