Combining two Weibull distributions using a mixing parameter

Ahmad Mahir Razali, Ali A. Salih

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

The aim of this paper is to introduce a method of combining two Weibull distributions. It shows how to produce a mixture distribution by including a mixing parameter which represents the proportions of mixing of the two component Weibull distributions. The mixture distribution produced from the combination of two or more Weibull distributions has a number of parameters. These parameters include; the shape parameters, scale parameters, location parameters in addition to the mixing parameter (w). A mixture distribution is even more useful because multiple causes of failure can be simultaneously modeled. In this paper we combined two Weibull distributios; the first with two parameters, shape and scale and the second with three parameters; shape, scale and location to obtain a mixture Weibull distribution with six parameters. We concentrated on the estimation of the mixing parameter and the parameters of the mixture Weibull distribution using maximum likelihood estimation. In addition we found the probability density function, cumulative distribution function, reliability function and failure rate of the mixture Weibull distribution. The mixing parameter (w; 0<w<1,) can take different values in the same distribution, Σw=1. Also, these values vary from one distribution to the other. We noticed the variety in the functions when we took different values for the mixing parameter; w=0.10, w=0.40, and w=0.8. Also these functions were represented by graphs that showed this variation. The estimation of parameters were effected by the different values of the mixing parameter.

Original languageEnglish
Pages (from-to)296-305
Number of pages10
JournalEuropean Journal of Scientific Research
Volume31
Issue number2
Publication statusPublished - 2009

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Weibull distribution
Weibull Distribution
Mixture Distribution
cumulative distribution
Maximum likelihood estimation
parameter
distribution
Probability density function
Distribution functions
Reliability Function
Location Parameter
Cumulative distribution function
Weibull
Failure Rate
Shape Parameter
Scale Parameter
Maximum Likelihood Estimation
Two Parameters
Proportion
probability density function

Keywords

  • Mixing parameter
  • Mixture Weibull distribution
  • Weibull distribution

ASJC Scopus subject areas

  • General

Cite this

Combining two Weibull distributions using a mixing parameter. / Razali, Ahmad Mahir; Salih, Ali A.

In: European Journal of Scientific Research, Vol. 31, No. 2, 2009, p. 296-305.

Research output: Contribution to journalArticle

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