Cdf.Chi Method

Evaluates the chi-squared cumulative probability distribution function.

public static double Chi(
double chsq,
double df
);

Parameters

chsq: A double specifying the argument at which the function is to be evaluated.
df: A double specifying the number of degrees of freedom. This must be at least 0.5.

Return Value

A double specifying the probability that a chi-squared random variable takes a values less than or equal to chsq.

Remarks

Method Chi evaluates the distribution function, F, of a chi-squared random variable with df degrees of freedom, that is, with $v = {\rm df}$ , and $x = {\rm chsq}$ ,

$F\left( x \right) = \frac{1}{{2^{\nu /2} \Gamma \left( {\nu /2} \right)}} \int_0^x {e^{ - t/2} t^{\nu /2 - 1} } dt$

where $\Gamma (\cdot)$ is the gamma function. The value of the distribution function at the point x is the probability that the random variable takes a value less than or equal to x.

For $v \gt 65$ , Chi uses the Wilson-Hilferty approximation (Abramowitz and Stegun 1964, equation 26.4.17) to the normal distribution, and method Normal is used to evaluate the normal distribution function.

For $v \le 65$ , Chi uses series expansions to evaluate the distribution function. If $x \lt \max (v/2, 26)$ , Chi uses the series 6.5.29 in Abramowitz and Stegun (1964), otherwise, it uses the asymptotic expansion 6.5.32 in Abramowitz and Stegun.

Plot of Chi-Squared Distribution Function

For greater right tail accuracy, Cdf.ComplementaryChi.

Cdf.Chi Method

Parameters

Return Value

Remarks

See Also