Logarithm Transformed Lomax Distribution with Applications. Issue 2 (November 2018)

• Record Type: Journal Article
• Authors: Nassar, Mazen; Dey, Sanku; Kumar, Devendra
• Is Part Of: Calcutta Statistical Association bulletin. Volume 70:Issue 2(2018:Nov.)
• Page Start: 122
• Page End: 135
• Publication Date: 2018-11
• Subjects: Conditional moments -- Lomax distribution -- logarithm transformed distribution -- maximum likelihood estimators; Mathematical statistics -- Periodicals; Statistics -- Methodology -- Periodicals; Statistics -- Periodicals; 519.5
• DOI: 10.1177/0008068318808135
• Languages: English
• ISSNs: 0008-0683

Abstract

In this article, we introduce a new method for generating distributions which we refer to as logarithm transformed (LT) method. Some statistical properties of the LT method are established. Based on the LT method, we introduce a new generalization of the Lomax distribution that provides better fits than the Lomax distribution and some of its known generalizations. We refer to the new distribution as logarithmic transformed Lomax (LTL) distribution. Various properties of the LTL distribution, including explicit expressions for the moments, quantiles, moment generating function, incomplete moments, conditional moments, Rényi entropy, and order statistics are derived. It appears to be a distribution capable of allowing monotonically decreasing and upside-down bathtub shaped hazard rates depending on its parameters, so it turns out to be quite flexible for analysing non-negative real life data. We discuss the estimation of the model parameters by maximum likelihood method using random censoring scheme. The proposed distribution is utilized to fit a censored data set and the distribution is shown to be more appropriate to the data set than the compared distributions. 2010 Mathematics Subject Classification: 60E05, 60E10, 62E15.