Abstract
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.
Highlights
Multi-parameter distributions to model lifetime data have been introduced by compounding a continuous lifetime and powerseries distributions
In this study a new lifetime class with decreasing failure rate is introduced by compounding truncated logarithmic distribution with any proper continuous lifetime distribution
Situations where the failure rate function decreases with time have been reported by several authors
Summary
Multi-parameter distributions to model lifetime data have been introduced by compounding a continuous lifetime and powerseries distributions. The Exponential Geometric (EG), Exponential Poisson (EP) and exponential logarithmic distributions were introduced and studied by Adamidis and Loukas (1998), Kus (2007) and Tahmasbi and Rezaei (2008), respectively. A two-parameter distribution family with decreasing failure rate arising by mixing power-series distribution has been introduced by Chahkandi and Ganjali (2009). A Weibull power series class of distributions with Poisson presented by Morais and Barreto-Souza (2011). In this study we generalize the work of Tahmasbi and Rezaei (2008) to a class of several lifetime continuous distributions and any mixture of continuous lifetime with truncated logarithmic distribution such as exponential, weibull, pareto becomes a special case of this class. The new class of logarithmic lifetime distributions with its probability and distribution functions are introduced. The entropy for the logarithmic lifetime distributions class is discussed
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