An approach to non-homogenous phase-type distributions through multiple cut-points

TL;DR

This paper introduces a new class of non-homogeneous phase-type distributions with multiple cut-points, providing improved modeling of lifetime data, especially heavy-tailed distributions, through a novel EM-algorithm and applications in resistive memory devices.

Contribution

It extends phase-type distributions to multiple cut-points, develops a new EM-algorithm for parameter estimation, and demonstrates improved fit and reduced parameters in modeling lifetime data.

Findings

Enhanced modeling of heavy-tailed distributions.

Reduced number of parameters in estimation.

Better fit compared to classical phase-type distributions.

Abstract

A new class of distributions based on phase-type distributions is introduced in the current paper to model lifetime data in the field of reliability analysis. This one is the natural extension of the distribution proposed by Acal et al. (2021) for more than one cut-point. Multiple interesting measures such as density function, hazard rate or moments, among others, were worked out both for the continuous and discrete case. Besides, a new EM-algorithm is provided to estimate the parameters by maximum likelihood. The results have been implemented computationally in R and simulation studies reveal that this new distribution reduces the number of parameters to be estimated in the optimization process and, in addition, it improves the fitting accuracy in comparison with the classical phase-type distributions, especially in heavy tailed distributions. An application is presented in the context of resistive memories with a new set of electron devices for non-volatile memory circuits. In particular, the voltage associated with the resistive switching processes that control the internal behaviour of resistive memories has been modelled with this new distribution to shed light on the physical mechanisms behind the operation of these memories.