Generating Student’s T Variates by a Modified Rejection Method

Ernst Stadlober
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Ernst Stadlober: Technical University Graz, Institute of Statistics

A chapter in Probability and Statistical Inference, 1982, pp 349-360 from Springer

Abstract: Abstract A new algorithm for sampling from Student’s ta distributions with parameter a > 3 is presented. The method is based on a modified acceptance-rejection technique introduced in 1981 by J.H. Ahrens for sampling from the gamma distribution. A suitable linear transformation of a ta-variate yields a probability density close to the t3 density. The final algorithm begins by sampling from this t3 distribution; it is able to accept and transform the initial t3-deviate quickly in 86 percent of the cases. In at least 6.6 percent of the cases only a quotient of modified t densities has to be compared with a uniform deviate. In the few remaining cases the transformed t3-deviate is rejected and a new deviate from the difference distribution has to be generated. The resulting accurate method is faster than competing algorithms if the parameter a changes frequently.

Keywords: Gamma Variable; Generate Student; Generate Random Variable; Basic Sampling Method; Final Algorithm (search for similar items in EconPapers)
Date: 1982
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-7840-9_33

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DOI: 10.1007/978-94-009-7840-9_33

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