Product Convolution of Generalized Subexponential Distributions

Gustas Mikutavičius and Jonas Šiaulys ()
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Gustas Mikutavičius: Institute of Mathematics, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania
Jonas Šiaulys: Institute of Mathematics, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania

Mathematics, 2023, vol. 11, issue 1, 1-11

Abstract: Assume that ξ and η are two independent random variables with distribution functions F ξ and F η , respectively. The distribution of a random variable ξ η , denoted by F ξ ⊗ F η , is called the product-convolution of F ξ and F η . It is proved that F ξ ⊗ F η is a generalized subexponential distribution if F ξ belongs to the class of generalized subexponential distributions and η is nonnegative and not degenerated at zero.

Keywords: tail function; closure property; product-convolution; generalized subexponential distribution; heavy-tailed distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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