Generating random variables with a $t$-distribution

Abstract:

Let RNOR and REXP represent normal and exponential random variables produced by computer subroutines. Then this simple algorithm may be used to generate a random variable T with ${t_n}$ density $c(1 + {t^2}/n)^{- 1/2 n - 1/2}$, for any $n > 2$: Generate $A = \mathrm {RNOR}, B = A^2/(n - 2)$ and $C = \mathrm {REXP}/ 1/2 n - 1)$ until $e^{ - B - C} \leqslant 1 - B$, then exit with $T = A[(1 - 2/n)(1 - B)]^{-1/2}$.