Turkish Journal of Mathematics
Abstract
We consider a classical semi-Markovian stochastic model of type $(s,S)$ with Logistic distributed demand random variables. Logistic distribution is a member of special distribution class known as $\Gamma(g)$ that encounters in many real-life applications involving extreme value theory. The objective of this study is to observe some major characteristics of a stochastic process $X(t)$ which represents semi-Markovian renewal reward process of type $(s,S)$. We used new approximation results for renewal function that allow us to obtain three-term asymptotic expansion for ergodic distribution function and for $n^{th}$ order moments of ergodic distribution of the process $X(t)$.
DOI
10.3906/mat-2002-72
Keywords
Logistic distribution, $\Gamma(g)$ class of distributions, heavy tailed distributions, semi-Markovian inventory model, ergodic distribution
First Page
1250
Last Page
1262
Recommended Citation
KAMIŞLIK, A. B, ALAKOÇ, B, KESEMEN, T, & KHANİYEV, T (2020). A semi-Markovian renewal reward process with $\Gamma(g)$ distributed demand. Turkish Journal of Mathematics 44 (4): 1250-1262. https://doi.org/10.3906/mat-2002-72
