Evaluates the chi-squared cumulative probability distribution function.

Namespace: Imsl.Stat
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.0.0

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.

See Also