Mixture of discrete weibull model

A. A. Al-Wakeel, Ahmad Mahir Razali

Research output: Contribution to journalArticle

Abstract

There are few studies on the mixture of discrete distributions, where most of the studies introduced a mixture of negative binomial, Poisson and binomial distributions. Recently, a sequence of studies on the mixture discrete distributions were published, but still very few. This paper introduced the new idea of mixture of discrete Weibull models. These models can be obtained by combining two or more discrete Weibull distributions using a mixing parameter. These models contain five or more parameters because each discrete Weibull contains two shape parameters q and β where 0<q<1 and β>0 and a mixing parameter w>0. In this paper, the distribution function, hazard (failure rate) function and second failure rate, called pseudo -hazard function of the mixture of discrete Weibull distribution were found using different values for the shape parameters and the mixing parameters. The distribution functions, hazard (failure rate) functions and pseudo- hazard functions were plotted depending on the data tables. It was found that the hazard (failure rate) functions and the pseudo-hazard functions can be increasing, decreasing or constant depending on the value of the shape parameter β, similar to the continuous Weibull distribution. Different values of the mixing parameter and the shape parameter were considered.

Original languageEnglish
Pages (from-to)580-586
Number of pages7
JournalAustralian Journal of Basic and Applied Sciences
Volume5
Issue number3
Publication statusPublished - Mar 2011

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Hazards
Weibull distribution
Distribution functions

Keywords

  • Discrete weibull
  • Hazard
  • Mixture weibull
  • Pseudo-hazard

ASJC Scopus subject areas

  • General

Cite this

Al-Wakeel, A. A., & Razali, A. M. (2011). Mixture of discrete weibull model. Australian Journal of Basic and Applied Sciences, 5(3), 580-586.

Mixture of discrete weibull model. / Al-Wakeel, A. A.; Razali, Ahmad Mahir.

In: Australian Journal of Basic and Applied Sciences, Vol. 5, No. 3, 03.2011, p. 580-586.

Research output: Contribution to journalArticle

Al-Wakeel, AA & Razali, AM 2011, 'Mixture of discrete weibull model', Australian Journal of Basic and Applied Sciences, vol. 5, no. 3, pp. 580-586.
Al-Wakeel, A. A. ; Razali, Ahmad Mahir. / Mixture of discrete weibull model. In: Australian Journal of Basic and Applied Sciences. 2011 ; Vol. 5, No. 3. pp. 580-586.
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