Polar generation of random variates with the 𝑡-distribution

Bailey, Ralph W.

doi:10.1090/S0025-5718-1994-1219702-8

Polar generation of random variates with the $t$-distribution
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by Ralph W. Bailey PDF

Math. Comp. 62 (1994), 779-781 Request permission

Abstract:

The "polar" method of Box and Muller uses two independent uniform variates in order to generate two independent normal variates. It can be adapted so that two variates from Student’s t-distribution with parameter $\nu$ are generated, though the two variates are now not independent. An algorithm based on the polar method is exact, inexpensive, and valid for all $\nu > 0$.

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