A New Generalization of the Extended Exponential Distribution with an Application

We introduce a new lifetime distribution namely, transmuted extended exponential distribution which generalizes the extended exponential distribution proposed by Nadarajah and Haghighi (Statistics 45:543–558, 2011) with an additional parameter using the quadratic rank transmutation map which was studied by Shaw and Buckley (The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map, 2009. arXiv:​0901.​0434) to provide greater flexibility in modeling data from a practical point of view. In this paper, our main focus is on estimation from frequentist point of view, yet, some statistical and reliability characteristics for the model are derived. We briefly describe different estimation procedures namely, the method of maximum likelihood estimation, maximum product of spacings estimation and least square estimation. Monte Carlo simulations are performed to compare the performance of the proposed methods of estimations for both small and large samples. Finally, the potentiality of the model is analyzed by means of one real data set.