On a new flexible Lomax distribution: statistical properties and estimation procedures with applications to engineering and medical data

This paper introduces a new extension of the traditional Lomax distribution. The current distribution, which has one scale and two shape parameters, is known as logarithmic transformed Lomax distribution. The hazard rate function of the new distribution based on parameter values, making monotonically decreasing, upside-down and bathtub upside-down shaped. Some properties of the proposed distribution including mixture expansion, moments, entropies, probability weighted moments, order statistics, reversed failure rate and mean past life time are discussed. The distribution parameters are estimated using four frequentist methods: namely, maximum likelihood, least squares, weighted least squares, and maximum product of spacing. The efficiency of the different estimators is compared using a simulation analysis using mean square error. Finally, two real data sets for service times of Aircraft Windshield and survival times of a group of patients given chemotherapy medication are analyzed and compared to some other competing distributions. Based on the results of data analysis, the estimates of minimum and maximum values for the service times of Aircraft Windshield and the survival times of patients given chemotherapy medication are obtained.