randomStudentT¶

Generates pseudorandom numbers from a Student’s t distribution.

Synopsis¶

randomStudentT (nRandom, df)

Required Arguments¶

int nRandom (Input): Number of random numbers to generate.
float df (Input): Degrees of freedom. Parameter df must be positive.

Return Value¶

An array of length nRandom containing the random deviates of a Student’s t distribution.

Optional Arguments¶

mean, float (Input): Mean of the Student’s t distribution.Default: mean = 0.0
variance, float (Input): Variance of the Student’s t distribution.Default: variance = 1.0

Description¶

Function randomStudentT generates pseudorandom numbers from a Student’s t distribution with df degrees of freedom, using a method suggested by Kinderman et al. (1977). The method (“TMX” in the reference) involves a representation of the t density as the sum of a triangular density over (−2, 2) and the difference of this and the t density. The mixing probabilities depend on the degrees of freedom of the t distribution. If the triangular density is chosen, the variate is generated as the sum of two uniforms; otherwise, an acceptance/rejection method is used to generate the difference density.

Example¶

In this example, randomStudentT generates five pseudorandom deviates from a Student’s t distribution with 12 degrees of freedom.

from numpy import *
from pyimsl.stat.randomStudentT import randomStudentT
from pyimsl.stat.randomSeedSet import randomSeedSet
from pyimsl.stat.writeMatrix import writeMatrix

n_random = 5
df = 5.0
randomSeedSet(123457)
r = randomStudentT(n_random, df)
writeMatrix("StudentT random deviates", r, noColLabels=True)

Output¶

 
                   StudentT random deviates
      0.615        1.189        0.091        1.377       -0.965