On Generating Distributions with the Memoryless Property

Kimihiro Noguchi and Koby F. Robles

The American Statistician, 2022, vol. 76, issue 3, 280-285

Abstract: The exponential and geometric distribution are well-known continuous and discrete family of distributions with the memoryless property, respectively. The memoryless property is emphasized in introductory probability and statistics textbooks even though no distribution beyond these two families of distributions has been explored in detail. By examining the relationship between these two families of distributions, we propose a general algorithm for generating distributions with the memoryless property. Then, we show that the general algorithm uniquely determines the distribution with the memoryless property given the parameter value, and nonnegative support which contains zero and is closed under addition. Furthermore, we present a few nontrivial examples and their applications to demonstrate the richness of such distributions.

Date: 2022
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DOI: 10.1080/00031305.2021.2006782

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