Statistical estimates in semi-Markovian inventory systems with heavy-tailed demand structure

Heavy-tailed distributions are frequently observed in problems related to inventory systems. It is known that the tails of random variables that express demand quantities have significant effects on inventory systems. In order to predict long term effects of unexpected demand fluctuations on these systems, inventory control models with heavy tailed demand quantities should be analyzed statistically. The purpose of this study is to examine the applicability of extreme value theory, which has been used effectively in many fields from medicine to insurance problems, to inventory systems as a statistically and mathematically sound research method with an application.In this context, statistical estimators based on extreme value theory for renewal functions will be investigated.A semi-Markovian inventory control model with a heavy-tailed demand, which tends to produce extreme values, will be considered and statistical estimators based on extreme value theory will be proposed for some characteristics of the stochastic process expressing the model.Then, the consistency and asymptotic normality properties of these estimators will be investigated.