Computer methods for sampling from Student’s 𝑡 distribution

Abstract

Several new algorithms for generating deviates from the <italic>t</italic> family for the degrees of freedom parameter <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="greater-than-or-slanted-equals 1"> <mml:semantics> <mml:mrow> <mml:mo>⩾</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">\geqslant 1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are presented. Both acceptance-rejection and probability mixing procedures are developed. The new algorithms outperform traditional methods for generating deviates from the <italic>t</italic> family. Recommendations are made concerning choosing an algorithm suited to its application.