A new family of contiuous distributions with three additional parameters, which ensure model flexiblity, is introduced based on the Fréchet distribution, also known as inverse Weibull distribution, and Topp-Leone family, which is presented by [8]. Two special models of the new family generator are discussed. We provide some distributional properties of this family in general setting such the series expansions of density, moments, generating function, stress strength model, Rényi and Shanon entropies, probability weighted moments and order statistics. Certain characterizations of the proposed family are presented based on well-known some statistical definitions. The maximum likelihood estimations procedure and the observed information matrix are obtained for the model parameters. We assess the performance of the maximum likelihood estimators by means of the simulation study graphically. The potentiality of the new class is shown via two applications to real data sets. |
