On using Shannon entropy measure for formulating new weighted exponential distribution

Abstract

In this article, a new class of weighted exponential distribution called Entropy-Based Exponential weighted distribution (EBEWD) is proposed. The main idea of the new lifetime distribution is in using the Shannon entropy measure as a weighted function. The mathematical properties of the EBEWD, such as reliability measures, moment measures, variability measures, shapes measures, entropy measures and Fisher’s information, were derived. The unknown parameters of the proposed distribution were estimated using the maximum likelihood estimation method. The efficiency and flexibility of the EBEWD were examined numerically and then by a real-life data application. The results revealed that the EBEWD outperforms some existing distributions in terms of their test statistics.

Keywords

• Exponential distribution
• weighted distribution
• entropy
• distribution theory
• goodness of fit