Automated phase-type distribution fitting via expectation maximization

In numerous practical domains such as reliability and performance engineering, finance, healthcare, and supply chain management, a common challenge revolves around accurately modeling intricate time-based data and event duration. The inherent complexities of real-world systems often make it challenging to use conventional statistical distributions. The phase-type (PH) distributions emerge as a remarkably adaptable class of distributions suited for modeling scenarios like failure or response times. These distributions are helpful in analytical and simulation-driven system evaluation approaches and are frequently used to fit empirical datasets. This paper introduces a strategy that leverages user-friendly tools, graphical adjustment features, and integration with existing tools to streamline the process of fitting PH distributions to empirical data. The simplicity of this procedure empowers domain experts to more accurately model complex systems, resulting in enhanced decision-making, more efficient resource allocation, improved reliability assessments, and optimized system performance across an extensive spectrum of practical domains where the analysis of time-based data remains pivotal. Furthermore, this study presents a method for the automated determination of parameters within a fitted Hyper-Erlang distribution. This method utilizes the Bayesian Information Criterion (BIC) within a Bayesian optimization framework integrated into an Expectation-Maximization (EM) algorithm. Consequently, it enables deriving a given dataset’s probability density function (PDF) through a combination of Hyper-Erlang distributions. Subsequently, the PDF serves as a tool for assessing system performance.