The Marshall-Olkin logistic-exponential distribution

M. Mansoor, M. H. Tahir, Gauss M. Cordeiro, Serge B. Provost, Ayman Yousef Abdelfattah Alzaatreh

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


We introduce a three-parameter extension of the exponential distribution which contains as sub-models the exponential, logistic-exponential and Marshall-Olkin exponential distributions. The new model is very flexible and its associated density function can be decreasing or unimodal. Further, it can produce all of the four major shapes of the hazard rate, that is, increasing, decreasing, bathtub and upside-down bathtub. Given that closed-form expressions are available for the survival and hazard rate functions, the new distribution is quite tractable. It can be used to analyze various types of observations including censored data. Computable representations of the quantile function, ordinary and incomplete moments, generating function and probability density function of order statistics are obtained. The maximum likelihood method is utilized to estimate the model parameters. A simulation study is carried out to assess the performance of the maximum likelihood estimators. Two actual data sets are used to illustrate the applicability of the proposed model.

Original languageEnglish
Pages (from-to)1-15
Number of pages15
JournalCommunications in Statistics - Theory and Methods
Publication statusAccepted/In press - Jan 4 2018


  • Censored data
  • Logistic distribution
  • Logistic-exponential distribution
  • Marshall-Olkin family
  • Maximum likelihood estimation

ASJC Scopus subject areas

  • Statistics and Probability

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