The modified Weibull geometric distribution

Min Wang, Ibrahim Elbatal

Research output: Contribution to journalJournal articlepeer-review

10 Scopus citations


A new class of lifetime distributions is introduced by compounding the modified Weibull and geometric distributions, the so-called modified Weibull geometric distribution. It includes as special submodels such as linear failure rate geometric distribution, Weibull geometric distribution, exponential geometric distribution, among others. We study its structural properties including probability density function, hazard functions, moments, generating and quantile functions. The distribution is capable of monotonically increasing, decreasing, bathtub-shaped, and upside-down bathtub-shaped hazard rates. Estimation by maximum likelihood and inference for a large sample are presented. An expectation-maximization algorithm is used to determine the maximum likelihood estimates of the parameters. Finally, a real data set is analyzed for illustrative purposes.

Original languageEnglish
Pages (from-to)303-315
Number of pages13
Issue number3
StatePublished - 1 Dec 2015
Externally publishedYes


  • EM algorithm
  • Geometric distribution
  • Hazard function
  • Maximum likelihood estimation
  • Modified Weibull distribution


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