Syntax

C#
public static double Chi( double chsq, double df )

Visual Basic (Declaration)
Public Shared Function Chi ( _ chsq As Double, _ df As Double _ ) As Double

Visual C++
public: static double Chi( double chsq, double df )

Parameters

chsq: Type: System..::.Double
A double specifying the argument at which the function is to be evaluated.

df: Type: System..::.Double
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 Cdf.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 $v\gt 343$ , Cdf.Chi uses the Wilson-Hilferty approximation (Abramowitz and Stegun 1964, equation 26.4.17) to the normal distribution, and method Cdf.Normal is used to evaluate the normal distribution function.

For $v\le 343$ , Cdf.Chi uses series expansions to evaluate the distribution function. If $x\lt\max(v/2, 26)$ , Cdf.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, see Cdf.ComplementaryChi.

Syntax

Parameters

Return Value

Remarks

See Also