Journal of Mathematics and Statistics

New Family of Logarithmic Lifetime Distributions

Said Hofan Alkarni

DOI : 10.3844/jmssp.2012.435.440

Journal of Mathematics and Statistics

Volume 8, Issue 4

Pages 435-440


In this study a new lifetime class with decreasing failure rate is introduced by compounding truncated logarithmic distribution with any proper continuous lifetime distribution. The properties of the proposed class are discussed, including a formal proof of itsprobability density function, distribution function and explicit algebraic formulae for its reliability and failure rate functions. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented. A formal equation for Fisher information matrix is derived in order to obtaining the asymptotic covariance matrix. Thisnew class of distributions generalizes several distributions which have been introduced and studied in the literature.


© 2012 Said Hofan Alkarni. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.