Bounded Weighted Exponential Distribution with Applications

Abstract

In this article, we try to supplement the distribution theory literature by incorporating a new bounded distribution, called the bounded weighted exponential (BWE) distribution in the (0, 1) intervals by transformation method. The proposed distribution exhibits decreasing and left-skewed unimodal density while the hazard rate can have increasing and bathtub shaped. Although our main focus is on the estimation from the frequentist point of view, in addition, we derive some useful structural and statistical properties of the proposed BWE distribution. We briefly describe three classical estimators namely, the maximum likelihood estimators (MLE), the ordinary least-squares estimators (LSE) and the weighted least-squares estimators (WLSE). Monte Carlo simulations are performed to compare performances of the proposed methods of estimation for both moderate and large samples. An application of the model is presented by re-analyzing a real data set and comparisons are made with the fit attained by some other well-known distributions for illustrative purposes.

KEYWORDS AND PHRASES::

• Least-squares estimators
• maximum likelihood estimators
• Monte Carlo simulation
• weighted exponential distribution
• weighted least-squares estimators