Unit extended exponential distribution with applications

Abstract

In this paper, the unit extended exponential distribution is presented. The extended exponential distribution is a two-parameter lifespan distribution that has been demonstrated to be very adaptable. Our goal is to convert this flexibility between the unit interval and the extended exponential distribution. Several different types of probability density functions, including decreasing, left-skewed, right-skewed, and unimodal, have been shown. However, the hazard rate function may take on various forms, including J-shaped, U-shaped, and bathtub shapes. A few statistical properties, such as moments, mean, variance, skewness, kurtosis, expectation-weighted moments, incomplete moments, conditional moments, mean deviation, Lorenz and Bonferroni curves, mean residual life, mean inactivity time, and various entropy measures, round out the theoretical section. The maximum likelihood technique is utilized to estimate model parameters using unit data. This study provides simulation data to evaluate the proposed strategy. Two applications utilizing actual data sets emphasize the significance of the new model compared to existing unit models.