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An Upside-Down Bathtub-Shaped Failure Rate Model Using a DUS Transformation of Lomax Distribution
Published in Lirong Cui, Ilia Frenkel, Anatoly Lisnianski, Stochastic Models in Reliability Engineering, 2020
Use of heavy-tailed distribution required for many of the lifetime data analysis. Pareto distribution is one of the heavy-tailed distributions which usually models non-negative data. This was introduced by Pareto (1897) as a model for the distribution of incomes. Several different forms of Pareto distribution have been studied by many authors, including Lomax (1954), Davis and Feldstein (1979), Grimshaw (1993) and Nadarajah and Gupta (2008). One of the popular hierarchies of Pareto distribution is Pareto Type II, also known as a Lomax distribution. The Lomax distribution has been applied to a variety of fields such as engineering, reliability, and life testing. In this chapter, we introduce a DUS transformation of Lomax distribution which exhibits a UBT-shaped failure rate function.
Parameter estimation of the Lomax distribution using genetic algorithm based on the ranked set samples
Published in Enterprise Information Systems, 2023
Lomax distribution, also called Pareto distribution of the second kind, was proposed by Lomax (1954). The distribution has been used for modelling different data such as engineering, medical and biological sciences, service times, use and supply times of products, income and wealth data, business failure data, similar variables in enterprise information systems. One of the most famous parametric models with these peculiarities is the Lomax distribution, a two-parameter family of distributions with the cumulative distribution function (cdf) and probability density function (pdf) expressed as