Statistical inference for a general class of distributions with time-varying parameters

Abstract

In this article we are interested in a general class of distributions for independent not necessarily identically distributed random variables, closed under minima, that includes a number of discrete and continuous distributions like the Geometric, Exponential, Weibull or Pareto. The main parameter involved in this class of distributions is assumed to be time varying with several possible modeling options. This is of particular interest in reliability and survival analysis for describing the time to event or failure. The maximum likelihood estimation of the parameters is addressed and the asymptotic properties of the estimators are discussed. We provide real and simulated examples and we explore the accuracy of the estimating procedure as well as the performance of classical model selection criteria in choosing the correct model among a number of competing models for the time-varying parameters of interest.

Keywords:

• Time-varying parameters
• parametric estimation
• model selection
• failure times

Acknowledgments

The authors wish to express their thanks to professor N Limnios for of Alliance Sorbonne Université, Université de Technologie de Compiègne, France for pointing out a mistake in a previous version of the paper. Finally, the authors wish to express their appreciation to the Editor and two Anonymous referees whose constructive comments and recommendations greatly improve both the quality and the presentation of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research work of Andreas Makrides was supported by FEDER funding within the framework of the project MOUSTIC–Random Models and Statistical, Informatics and Combinatorics Tools (2016–2019) from the Region of Normandy, France, through a postdoctoral position in Laboratory of Mathematics Raphaël Salem, Department of Mathematics, University of Rouen Normandy. The research work of Vlad Stefan Barbu was partially supported by the same project MOUSTIC–Random Models and Statistical, Informatics and Combinatorics Tools (2016–2019) from the Region of Normandy, France. The research work of Alex Karagrigoriou was partially supported by the University of Rouen Normandy, France, by offering the opportunity of spending several periods as a visiting professor in the Laboratory of Mathematics Raphaël Salem, Department of Mathematics, University of Rouen Normandy. The same author wishes to acknowledge the support of the Laboratory of Statistics and Data Analysis of the University of the Aegean.