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 {t_n} density c ( 1 + t 2 / n ) − 1 / 2 n − 1 / 2 c(1 + {t^2}/n)^{- 1/2 n - 1/2} , for any n > 2 n > 2 : Generate A = R N O R , B = A 2 / ( n − 2 ) A = \mathrm {RNOR}, B = A^2/(n - 2) and C = R E X P / 1 / 2 n − 1 ) C = \mathrm {REXP}/ 1/2 n - 1) until e − B − C ⩽ 1 − B e^{ - B - C} \leqslant 1 - B , then exit with T = A [ ( 1 − 2 / n ) ( 1 − B ) ] − 1 / 2 T = A[(1 - 2/n)(1 - B)]^{-1/2} .