Polar generation of random variates with the 𝑡-distribution

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 ν \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 ν > 0 \nu > 0 .