Transmuted shifted exponential distribution and applications

Abstract

In this paper, we used the quadratic transmutation map approach to propose a new distribution model called the transmuted shifted exponential distribution (TSED). We derived some of its useful statistical properties such as the moment, Characteristic function, Quantile function, Shannon Entropy, relative entropy, Renyi entropy, moment generating function, mean inactivity function, hazard rate function, survival rate function, and the order statistics. The simulation results showed that as the sample size increases, the biases, variances, and root mean square errors become smaller for the censored sample. We used two life data sets to evaluate the numerical applications of the proposed TSED. The results obtained are compared with some existing probability distribution models. It is observed that the TSED gave a better fit to all the data sets under consideration than other models.

Subject Classification: (2010):

• 62E10
• 65C20
• 65C60
• 62P30

Keywords:

• Transmuted family of distribution
• Quantile function
• Mean inactivity function
• Relative entropy and order statistics