Statistics and Its Interface

Volume 9 (2016)

Number 2

A comparison of methods for estimating parameters of the type I discrete Weibull distribution

Pages: 203 – 212



Alessandro Barbiero (Department of Economics, Management and Quantitative Methods, Università degli Studi di Milano, Italy)


The type I discrete Weibull distribution can be used in reliability problems for modeling discrete failure data, such as the number of shocks, cycles, or runs a component or structure can overcome before failing. This paper refines and compares some existing methods for estimating its parameters and proposes and evaluates approximate confidence intervals for large samples. A Monte Carlo simulation study was performed in order to assess the statistical performance of the methods for different parameter combinations and sample sizes and then give some indication for their mindful use. Examples are considered as a practical application of the proposed procedures. A software implementation of the model is provided as a contributed package in the $\mathsf{R}$ programming environment, which reveals a useful and friendly tool for the researcher who has to handle discrete Weibull data.


failure data, maximum likelihood, method of moments, method of proportion, reliability

Published 4 November 2015