Theoretical results on the discrete Weibull distribution of Nakagawa and Osaki. Issue 2 (4th March 2019)

• Record Type: Journal Article
• Authors: Vila, Roberto; Nakano, Eduardo Y.; Saulo, Helton
• Is Part Of: Statistics. Volume 53:Issue 2(2019)
• Page Start: 339
• Page End: 363
• Publication Date: 2019-03-04
• Subjects: Discrete Weibull distribution -- confidence interval -- maximum likelihood -- Monte Carlo simulation; 62N02 -- 62Q05 -- 62F10 -- 62F12; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2018.1550645
• Languages: English
• ISSNs: 0233-1888

Abstract

ABSTRACT: In this paper, we discuss some theoretical results and properties of the discrete Weibull distribution, which was introduced by Nakagawa and Osaki [The discrete Weibull distribution. IEEE Trans Reliab. 1975;24:300–301]. We study the monotonicity of the probability mass, survival and hazard functions. Moreover, reliability, moments, p -quantiles, entropies and order statistics are also studied. We consider likelihood-based methods to estimate the model parameters based on complete and censored samples, and to derive confidence intervals. We also consider two additional methods to estimate the model parameters. The uniqueness of the maximum likelihood estimate of one of the parameters that index the discrete Weibull model is discussed. Numerical evaluation of the considered model is performed by Monte Carlo simulations. For illustrative purposes, two real data sets are analyzed.