Topp Leone Exponential – Generalized Inverted Exponential Distribution Properties and Application

Abstract

Abdulmuahymin Abiola Sanusi, Sani Ibrahim Doguwa, , and Abubakar Yahaya 

In this paper, a new distribution called Topp Leone Exponential – Generalized Inverted Exponential distribution (TLE-GIE)
is developed to improve on the flexibility of Topp Leone generalized inverted exponential (TL-GIE) distribution. The TLE-GIE
distribution was developed by extending the generalized inverted exponential distribution with Topp Leone Exponential G family of distribution. The respective density and distribution functions of this new distribution (TLE-GIE) were derived including some
mathematical properties such as moments, quantile function, renyi entropy and order statistics. A simulation study conducted, by the consideration of the Maximum Likelihood Estimate (MLE) method shows that the estimated parameters of TLE-GIE are consistent as the BIAS and RMSE approach zero. Finally, three real data sets were used to validate the results obtained from the MLE method. The results obtained indicated that the TLE-GIE distribution provided a better fitness of the data sets than the TL-GIE and other competitive distributions. Perhaps, this new distribution may be useful for the modelling real life data sets that may behave exponentially.