# Topp Leone Exponential – Generalized Inverted Exponential Distribution Properties and Application

## Keywords:

Topp Leone Exponential, Generalized Inverted Exponential distribution;, Mathematical properties, Simulation study, pplication to real life data sets.## Abstract

**Communication in Physical Sciences, 2022, 8(4):442-455**

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

Abubakar Yahaya

Received: 11 July 2022/Accepted 14 September 2022

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.

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