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The product t density distribution arising from the product of two Student’s t PDFs

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Abstract

The Student’s t distribution has become increasingly prominent and is considered as a competitor to the normal distribution. Motivated by real examples in Physics, decision sciences and Bayesian statistics, a new t distribution is introduced by taking the product of two Student’s t pdfs. Various structural properties of this distribution are derived, including its cdf, moments, mean deviation about the mean, mean deviation about the median, entropy, asymptotic distribution of the extreme order statistics, maximum likelihood estimates and the Fisher information matrix. Finally, an application to a Bayesian testing problem is illustrated.

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  1. School of Mathematics, University of Manchester, Manchester, M60 1QD, UK

    Saralees Nadarajah

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  1. Saralees Nadarajah
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Correspondence to Saralees Nadarajah.

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Nadarajah, S. The product t density distribution arising from the product of two Student’s t PDFs. Stat Papers 50, 605–615 (2009). https://doi.org/10.1007/s00362-007-0088-x

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  • DOI: https://doi.org/10.1007/s00362-007-0088-x

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