The logistic-X family of distributions and its applications. Issue 24 (16th December 2016)

• Record Type: Journal Article
• Authors: Tahir, M. H.; Cordeiro, Gauss M.; Alzaatreh, Ayman; Mansoor, M.; Zubair, M.
• Is Part Of: Communications in statistics. Volume 45:Issue 24(2016)
• Page Start: 7326
• Page End: 7349
• Publication Date: 2016-12-16
• Subjects: Estimation -- Fréchet distribution -- Logistic distribution -- Moment -- T-X family.; 60E05 -- 62F10 -- 62N05; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2014.980516
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: 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.