naginterfaces.library.stat.prob_​chisq

naginterfaces.library.stat.prob_chisq(x, df, tail='L')[source]

prob_chisq returns the lower or upper tail probability for the -distribution with real degrees of freedom.

For full information please refer to the NAG Library document for g01ec

https://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/g01/g01ecf.html

Parameters
xfloat

, the value of the variate with degrees of freedom.

dffloat

, the degrees of freedom of the -distribution.

tailstr, length 1, optional

Indicates whether the upper or lower tail probability is required.

The lower tail probability is returned, i.e., .

The upper tail probability is returned, i.e., .

Returns
pfloat

The lower or upper tail probability for the -distribution, depending on the value of supplied.

Raises
NagValueError
(errno )

On entry, .

Constraint: or .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

The series used to calculate the gamma probabilities has failed to converge. The result returned should represent an approximation to the solution.

Notes

The lower tail probability for the -distribution with degrees of freedom, is defined by:

To calculate a transformation of a gamma distribution is employed, i.e., a -distribution with degrees of freedom is equal to a gamma distribution with scale parameter and shape parameter .

References

NIST Digital Library of Mathematical Functions

Hastings, N A J and Peacock, J B, 1975, Statistical Distributions, Butterworth