cdfchi

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 — cumulative distribution function Beta distribution
• cdfbin — cumulative distribution function Binomial distribution
• cdfchn — cumulative distribution function non-central chi-square distribution
• cdff — cumulative distribution function Fisher 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