naginterfaces.library.rand.multivar_​students_​t

naginterfaces.library.rand.multivar_students_t(mode, n, df, xmu, c, comm, statecomm)[source]

multivar_students_t sets up a reference vector and generates an array of pseudorandom numbers from a multivariate Student’s distribution with degrees of freedom, mean vector and covariance matrix .

For full information please refer to the NAG Library document for g05ry

https://www.nag.com/numeric/nl/nagdoc_27.1/flhtml/g05/g05ryf.html

Parameters
modeint

A code for selecting the operation to be performed by the function.

Set up reference vector only.

Generate variates using reference vector set up in a prior call to multivar_students_t.

Set up reference vector and generate variates.

nint

, the number of random variates required.

dfint

, the number of degrees of freedom of the distribution.

xmufloat, array-like, shape

, the vector of means of the distribution.

cfloat, array-like, shape

Matrix which, along with , defines the covariance of the distribution. Only the upper triangle need be set.

commdict, communication object, modified in place

Communication structure for the reference vector.

If , this argument must have been initialized by a prior call to multivar_students_t.

statecommdict, RNG communication object, modified in place

RNG communication structure.

This argument must have been initialized by a prior call to init_repeat() or init_nonrepeat().

Returns
xNone or float, ndarray, shape

The array of pseudorandom multivariate Student’s vectors generated by the function, with holding the th dimension for the th variate.

Raises
NagValueError
(errno )

On entry, .

Constraint: , or .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, the covariance matrix is not positive semidefinite to machine precision.

(errno )

is not the same as when [‘r’] was set up in a previous call.

Previous value of and .

(errno )

On entry, [‘state’] vector has been corrupted or not initialized.

Notes

When the covariance matrix is nonsingular (i.e., strictly positive definite), the distribution has probability density function

where is the number of dimensions, is the degrees of freedom, is the vector of means, is the vector of positions and is the covariance matrix.

The function returns the value

where is generated by dist_normal() from a Normal distribution with mean zero and covariance matrix and is generated by dist_chisq() from a -distribution with degrees of freedom.

One of the initialization functions init_repeat() (for a repeatable sequence if computed sequentially) or init_nonrepeat() (for a non-repeatable sequence) must be called prior to the first call to multivar_students_t.

References

Knuth, D E, 1981, The Art of Computer Programming (Volume 2), (2nd Edition), Addison–Wesley

Wilkinson, J H, 1965, The Algebraic Eigenvalue Problem, Oxford University Press, Oxford