Affiliations: [a] Department of Statistics, University of Peshawar, KPK, Pakistan
| [b] Department of Statistics, University of Haripur, Haripur, KPK, Pakistan
| [c] Department of Statistics, Islamia College University, KPK, Pakistan
| [d] Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj, Saudi Arabia
| [e] Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt
Correspondence:
[*]
Corresponding author. Muhammad Ijaz, Department of Statistics, University of Haripur, Haripur, KPK, Pakistan. E-mail: ijaz.statistics@gmail.com.
Abstract: Statistical lifetime distributions play a very important role in modeling data sets in various fields. Extending the existing distributions is of great interest in statistical research. The modification of the distributions provides more flexible model as compared to existing one. In this article, we propose a new probability model using Quadratic Rank Transmutation Map technique, named as Transmuted Lomax Exponential Distribution (TLED). The new distribution can model data sets with increasing, decreasing and bathtub shape hazard rates. Various statistical properties of the proposed distribution such as moments, order statistics, quantile function, mean residual life function and characteristic function are derived. Further, the parameter estimates are obtained through Maximum Likelihood method along with asymptotic confidence intervals. The utility of the new model is evaluated by analyzing two real data sets. In order to access the performance of the new model, several goodness of fit measures is used. The results indicate that the new model best fits the data as compared to the other extensions of the Lomax distribution.
Keywords: Lomax distributions, maximum likelihood, transmuted, estimation, hazard function
