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The Memoryless Property and Moments of the Gumbel Distribution

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Abstract

The central moments of the extreme-value distribution, which is also called the Gumbel distribution, are derived. Its status as the limiting distribution of the largest order statistic of a random sample from a unit exponential distribution is employed for that purpose. The memoryless property of the exponential distribution plays a major role.

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Authors and Affiliations

  1. School of Mathematical Sciences, Rochester Institute of Technology, 84 Lomb Memorial Drive, Rochester, NY, 14623, USA

    James E. Marengo & David L. Farnsworth

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  1. James E. Marengo
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  2. David L. Farnsworth
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Correspondence to David L. Farnsworth.

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Marengo, J.E., Farnsworth, D.L. The Memoryless Property and Moments of the Gumbel Distribution. J Stat Theory Pract 16, 70 (2022). https://doi.org/10.1007/s42519-022-00296-2

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