Cdf.Chi Method

CdfChi Method

Evaluates the chi-squared cumulative probability distribution function.

Namespace: Imsl.Stat
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0

Syntax

public static double Chi(
	double chsq,
	double df
)

Public Shared Function Chi ( 
	chsq As Double,
	df As Double
) As Double

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

static member Chi : 
        chsq : float * 
        df : float -> float

Parameters

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

Return Value

Type: Double
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.

Reference

Cdf Class

Imsl.Stat Namespace

Other Resources

Example