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Generating Random Variables With a $t$-Distribution

George Marsaglia
Mathematics of Computation
Vol. 34, No. 149 (Jan., 1980), pp. 235-236
DOI: 10.2307/2006231
Stable URL: http://www.jstor.org/stable/2006231
Page Count: 2
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Abstract

Let $\mathrm{RNOR}$ and $\mathrm{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 $c(1 + t^2/n)^{-1/2n-1/2}$, for any $n > 2$: Generate $A = \mathrm{RNOR}, B = A^2/(n - 2)$ and $C = \mathrm{REXP}/(1/2n - 1)$ until $e^{-B-C} \leqslant 1 - B$, then exit with $T = A\lbrack(1 - 2/n)(1 - B)\rbrack^{-1/2}$.

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