naginterfaces.library.stat.prob_​chisq_​vector

naginterfaces.library.stat.prob_chisq_vector(tail, x, df)[source]

prob_chisq_vector returns a number of lower or upper tail probabilities for the -distribution with real degrees of freedom.

For full information please refer to the NAG Library document for g01sc

https://www.nag.com/numeric/nl/nagdoc_28.4/flhtml/g01/g01scf.html

Parameters
tailstr, length 1, array-like, shape

Indicates whether the lower or upper tail probabilities are required. For , for :

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

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

xfloat, array-like, shape

, the values of the variates with degrees of freedom.

dffloat, array-like, shape

, the degrees of freedom of the -distribution.

Returns
pfloat, ndarray, shape

, the probabilities for the distribution.

ivalidint, ndarray, shape

indicates any errors with the input arguments, with

No error.

On entry, invalid value supplied in when calculating .

On entry, .

On entry, .

The solution has failed to converge while calculating the gamma variate. The result returned should represent an approximation to the solution.

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

Warns
NagAlgorithmicWarning
(errno )

On entry, at least one value of , or was invalid, or the solution failed to converge.

Check for more information.

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 .

The input arrays to this function are designed to allow maximum flexibility in the supply of vector arguments by re-using elements of any arrays that are shorter than the total number of evaluations required. See the G01 Introduction for further information.

References

NIST Digital Library of Mathematical Functions

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