naginterfaces.library.stat.prob_​bivariate_​students_​t

naginterfaces.library.stat.prob_bivariate_students_t(df, rho, a=None, b=None)[source]

prob_bivariate_students_t returns probabilities for the bivariate Student’s -distribution.

For full information please refer to the NAG Library document for g01hc

https://www.nag.com/numeric/nl/nagdoc_28.4/flhtml/g01/g01hcf.html

Parameters
dfint

, the degrees of freedom of the bivariate Student’s -distribution.

rhofloat

, the correlation of the bivariate Student’s -distribution.

aNone or float, array-like, shape , optional

If upper tail or central probablilities are to be returned, should supply the lower bounds, , for .

bNone or float, array-like, shape , optional

If lower tail or central probablilities are to be returned, should supply the upper bounds, , for .

Returns
pfloat

The probabilities for the bivariate Student’s -distribution.

Raises
NagValueError
(errno )

On entry, .

Constraint: , or .

(errno )

On entry, for central probability, for some .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

Notes

Let the vector random variable follow a bivariate Student’s -distribution with degrees of freedom and correlation , then the probability density function is given by

The lower tail probability is defined by:

The upper tail probability is defined by:

The central probability is defined by:

Calculations use the Dunnett and Sobel (1954) method, as described by Genz (2004).

References

Dunnett, C W and Sobel, M, 1954, A bivariate generalization of Student’s -distribution, with tables for certain special cases, Biometrika (41), 153–169

Genz, A, 2004, Numerical computation of rectangular bivariate and trivariate Normal and probabilities, Statistics and Computing (14), 151–160