The logistic-X family of distributions and its applications

M. H. Tahir, Gauss M. Cordeiro, Ayman Alzaatreh, M. Mansoor, M. Zubair

Research output: Contribution to journalArticlepeer-review

49 Citations (Scopus)


The logistic distribution has a prominent role in the theory and practice of statistics. We introduce a new family of continuous distributions generated from a logistic random variable called the logistic-X family. Its density function can be symmetrical, left-skewed, right-skewed, and reversed-J shaped, and can have increasing, decreasing, bathtub, and upside-down bathtub hazard rates shaped. Further, it can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. We derive explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Bonferroni and Lorenz curves, Shannon entropy, and order statistics. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. We also investigate the properties of one special model, the logistic-Fréchet distribution, and illustrate its importance by means of two applications to real data sets.

Original languageEnglish
Pages (from-to)7326-7349
Number of pages24
JournalCommunications in Statistics - Theory and Methods
Issue number24
Publication statusPublished - Dec 16 2016


  • Estimation
  • Fréchet distribution
  • Logistic distribution
  • Moment
  • T-X family

ASJC Scopus subject areas

  • Statistics and Probability

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