Abstract
The present study introduces a new three-parameter model called the modified Kies–Lomax (MKL) distribution to extend the Lomax distribution and increase its flexibility in modeling real-life data. The MKL distribution, due to its flexibility, provides left-skewed, symmetrical, right-skewed, and reversed-J shaped densities and increasing, unimodal, decreasing, and bathtub hazard rate shapes. The MKF density can be expressed as a linear mixture of Lomax densities. Some basic mathematical properties of the MKF model are derived. Its parameters are estimated via six estimation algorithms. We explore their performances using detailed simulation results, and the partial and overall ranks are provided for the measures of absolute biases, mean square errors, and mean relative errors to determine the best estimation method. The results show that the maximum product of spacings and maximum likelihood approaches are recommended to estimate the MKL parameters. Finally, the flexibility of the MKL distribution is checked using two real datasets, showing that it can provide close fit to both datasets as compared with other competing Lomax models. The three-parameter MKL model outperforms some four-parameter and five-parameter rival models.
Highlights
Introduction eLomax distribution has several applications in different applied fields such as biological sciences, income and wealth inequality, engineering, reliability, and actuarial sciences
Okasha [10] studied the E-Bayesian estimation for the Lomax distribution based on type-II censored data and Hassan and Zaky [11] studied the entropy Bayesian estimation for the Lomax distribution based on records
Further important aim of the current paper is to explore the estimation of the modified Kies–Lomax (MKL) parameters using classical methods such as maximum likelihood, Anderson–Darling, Cramer–von Mises, least-squares, weighted least-squares, and maximum product of spacings
Summary
Introduction eLomax distribution has several applications in different applied fields such as biological sciences, income and wealth inequality, engineering, reliability, and actuarial sciences. E procedure of expanding classical distributions by adding new shape parameters is well-known technique in statistical literature. Various extensions of the Lomax distribution have been constructed using well-known generators to increase its flexibility in modeling various types of data. E new added shape parameters are important to provide skewness and to increase tail weights as well as to enhance the flexibility to model monotonic and nonmonotonic hazard rates if the baseline hazard rate is only monotonic. For more details about Bayesian inference for probability distributions, the interested reader can refer to [12,13,14,15,16,17,18,19]
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