A new flexible logarithmic transform heavy-tailed distribution and its applications

Abstract

This paper aims to propose a new right skewed, heavy tailed probability distribution with upside-down bathtub shape hazard rate. The related statistical characteristics and its measures are derived. The unknown parameter of the proposed distribution is estimated by using five estimation methods, namely maximum likelihood estimation (MLE) method, maximum product spacing estimation (MPSE) method, least square estimation (LSE) method, weighted least square estimation method and Cramer-Von-Mises estimation (CVME) method. Also, asymptotic confidence interval (ACI) and bootstrap confidence intervals (BCIs) namely, standard bootstrap (s-boot), percentile bootstrap (p-boot), and Student’s bootstrap (t-boot) of the parameter are also computed. The Monte Carlo simulation study has been performed to compare the performance of the proposed estimators and corresponding interval width along with coverage probability. At last, three real data sets have been used to demonstrate the suitability of the proposed study in real life scenario. The considered data sets also exhibit skewed, heavy tailed, upside-down bathtub shape hazard rate pattern.

Subject Classification:

• 62E10
• 60E05
• 62H10
• 62H12

Keywords:

• Heavy tailed distribution
• Stochastic order
• Order statistics
• Entropy measurement
• Different method of estimation