CdfComplementaryChi Method |
Calculates the complement of the chi-squared distribution.
Namespace: Imsl.StatAssembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0
Syntax public static double ComplementaryChi(
double chsq,
double df
)
Public Shared Function ComplementaryChi (
chsq As Double,
df As Double
) As Double
public:
static double ComplementaryChi(
double chsq,
double df
)
static member ComplementaryChi :
chsq : float *
df : float -> float
Parameters
- chsq
- Type: SystemDouble
A double scalar value at which 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 value greater than
chsq.
Remarks
Method
Cdf.ComplementaryChi evaluates the distribution function,
, of a chi-squared random variable with
df degrees of freedom, that is, with
, and
,
where is the gamma
function. The value of the distribution function at the point
x is the probability that the random variable takes a value
greater than x.
For , Cdf.ComplementaryChi uses the
Wilson-Hilferty approximation (Abramowitz and Stegun 1964, equation
26.4.17) to the one minus the normal distribution, and method
Cdf.Normal is used to evaluate the normal distribution function.
For , Cdf.ComplementaryChi
uses series expansions to evaluate the distribution function. If
, Cdf.ComplementaryChi uses
the series 6.5.29 in Abramowitz and Stegun (1964), otherwise, it
uses the asymptotic expansion 6.5.32 in Abramowitz and Stegun.
This function provides higher right tail accuracy for the
Chi-squared distribution.
See Also