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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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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DOI: https://doi.org/10.1007/s42519-022-00296-2
Keywords
- Gumbel distribution
- Exponential distribution
- Largest order statistic
- Memoryless property
- Moment
- Probabilistic proof