Topp-Leone exponential-Lomax distribution: Properties and applications

The Topp-Leone Exponential–Lomax (TLE–L) distribution is a new distribution developed with an improved flexibility when comparing its performance with some other existing and related distributions. This new TLE–L distribution was developed by extending the Lomax distribution with the Topp Leone Exponential G family of distributions. The density and distribution functions of this TLE–L distribution were defined, as well as some respective mathematical properties, such as moments, quantile function, Rényi entropy, and order statistics, which were all derived. The Maximum Likelihood Estimate (MLE) method was considered for the simulation study. The results show that the estimated parameters of this TLE–L distribution are consistent as the BIAS and RMSE approach zero. Also, the model flexibility indicator carried out on TLE – L distribution confirms that it is more flexible compared to its baseline distribution. Conclusively, the TLE–L distribution was applied to model two real data sets; this is done to validate the results obtained from the MLE method only. The results obtained show that the TLE–L distribution best fits the two data sets compared to other distributions used in this study. Possibly, TLE–L distribution would be more useful to fit and model positive real life data sets with the characteristics of high kurtosis and heavy tail towards right hand side (asymmetric data sets).