Estimating the parameters of mixed shifted negative binomial distributions via an EM algorithm

Varmazyar, M. and Akhavan, Raha and Salmasi, N. and Modarres, M. (2019) Estimating the parameters of mixed shifted negative binomial distributions via an EM algorithm. Scientia Iranica, 26 (1). pp. 571-588. ISSN 1026-3098 (Print) 2345-3605 (Online)

This is the latest version of this item.

Full text not available from this repository. (Request a copy)


Discrete Phase-Type (DPH) distributions have one property that is not shared by Continuous Phase-Type (CPH) distributions, i.e., representing a deterministic value as a DPH random variable. This property distinguishes the application of DPH in stochastic modeling of real-life problems, such as stochastic scheduling, in which service time random variables should be compared with a deadline that is usually a constant value. In this paper, we consider a restricted class of DPH distributions, called Mixed Shifted Negative Binomial (MSNB), and show its flexibility in producing a wide range of variances as well as its adequacy in fitting fat-tailed distributions. These properties render MSNB applicable to represent data on certain types of service time. Therefore, we adapt an Expectation-Maximization (EM) algorithm to estimate the parameters of MSNB distributions that accurately fit trace data. To present the applicability of the proposed algorithm, we use it to fit real operating room times and a set of benchmark traces generated from continuous distributions as case studies. Finally, we illustrate the efficiency of the proposed algorithm by comparing its results with those of two existing algorithms in the literature. We conclude that our proposed algorithm outperforms other DPH algorithms in fitting trace data and distributions.
Item Type: Article
Uncontrolled Keywords: Discrete Phase-Type (DPH) distributions; Expectation-Maximization (EM) algorithm; Mixed shifted negative binomial distributions; Parameter estimation
Divisions: Sabancı Business School
Depositing User: Raha Akhavan
Date Deposited: 31 Jul 2023 13:35
Last Modified: 31 Jul 2023 13:35

Available Versions of this Item

Actions (login required)

View Item
View Item