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A New Modified Inverse Lomax Distribution: Properties, Estimation and Applications to Engineering and Medical Data

Abdullah M. Almarashi*

Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

* Corresponding Author: Abdullah M. Almarashi. Email:

(This article belongs to this Special Issue: Modeling Real World Problems with Mathematics)

Computer Modeling in Engineering & Sciences 2021, 127(2), 621-643.


In this paper, a modified form of the traditional inverse Lomax distribution is proposed and its characteristics are studied. The new distribution which called modified logarithmic transformed inverse Lomax distribution is generated by adding a new shape parameter based on logarithmic transformed method. It contains two shape and one scale parameters and has different shapes of probability density and hazard rate functions. The new shape parameter increases the flexibility of the statistical properties of the traditional inverse Lomax distribution including mean, variance, skewness and kurtosis. The moments, entropies, order statistics and other properties are discussed. Six methods of estimation are considered to estimate the distribution parameters. To compare the performance of the different estimators, a simulation study is performed. To show the flexibility and applicability of the proposed distribution two real data sets to engineering and medical fields are analyzed. The simulation results and real data analysis showed that the Anderson-Darling estimates have the smallest mean square errors among all other estimates. Also, the analysis of the real data sets showed that the traditional inverse Lomax distribution and some of its generalizations have shortcomings in modeling engineering and medical data. Our proposed distribution overcomes this shortage and provides a good fit which makes it a suitable choice to model such data sets.


Cite This Article

Almarashi, A. M. (2021). A New Modified Inverse Lomax Distribution: Properties, Estimation and Applications to Engineering and Medical Data. CMES-Computer Modeling in Engineering & Sciences, 127(2), 621–643.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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