naginterfaces.library.rand.dist_students_t(n, df, statecomm)[source]

dist_students_t generates a vector of pseudorandom numbers taken from a Student’s -distribution with degrees of freedom.

For full information please refer to the NAG Library document for g05sn


, the number of pseudorandom numbers to be generated.


, the number of degrees of freedom of the distribution.

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().

xfloat, ndarray, shape

The pseudorandom numbers from the specified Student’s -distribution.

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

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


The distribution has PDF (probability density function)

dist_students_t calculates the values

where the are generated by dist_normal() from a Normal distribution with mean and variance , and the are generated by dist_gamma() from a gamma distribution with parameters and (i.e., 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 dist_students_t.


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