Abstract
In this work, we present a five-parameter life time distribution called Harris power Lomax (HPL)  distribution which is obtained by convoluting the Harris-G distribution and the Power Lomax distribution. When compared to the existing distributions, the new distribution exhibits a very flexible probability functions; which may be increasing, decreasing, J, and reversed J shapes been observed for the probability density and hazard rate functions. The structural properties of the new distribution are studied in detail which includes: moments, incomplete moment, Renyl entropy, order statistics, Bonferroni curve, and Lorenz curve etc. The HPL  distribution parameters are estimated by using the method of maximum likelihood. Monte Carlo simulation was carried out to investigate the performance of MLEs. Aircraft wind shield data and Glass fibre data applications demonstrate the applicability of the proposed model.
Highlights
In the last decades, the Lomax distribution introduced by Lomax (1954), has been discovered to be very useful in several areas of applications most especially in applied sciences such as applications in flood, queue theory, internet traffic control, life testing, wind speed, sea waves and many others
We present a five-parameter life time distribution called Harris power Lomax (HPL) distribution which is obtained by convoluting the Harris-G distribution and the Power Lomax distribution
We develop and study a new distribution called the Harris Power Lomax distribution which possesses these properties with a wide range of applications
Summary
The Lomax distribution introduced by Lomax (1954), has been discovered to be very useful in several areas of applications most especially in applied sciences such as applications in flood, queue theory, internet traffic control, life testing, wind speed, sea waves and many others. Aly and Benkherouf (2011) discoursed several properties of (6) and provided the basis for the generalization of the Marshall-Olkin class considering the pgf of the Harris distribution (Harris, 1948) for obtaining new distributions. This pgf is given by γ(s, c, v) = ̅ , v > 0. The chief motivation of this study is based on the advantages of the generalized distribution with respect to having a hazard function that exhibits decreasing, increasing and bathtub shapes as well as the flexibility gain in compounding Harris distribution and Power Lomax distributions in modeling real life data.
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