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This paper introduces a new one-parameter family (NPFD) derived from the cumulative distribution function (CDF). We study the main properties of the proposed family, with a special emphasis on its moments, reliability parameters, and asymptotic distributions of the extreme order statistics. Then, inferential considerations are explored. We discuss the parameter estimation by the moments, maximum likelihood methods and the Bayesian estimation. Also, likelihood estimation and Bayesian estimation using the Pitman asymptotic criterion are given. Three applications reveal that the new model can fit well practical data sets. [ABSTRACT FROM AUTHOR]

Modeling and analyzing lifespan data is essential in many application areas, including medicine, engineering, and finance. These types of data have been modeled using various lifetime distributions. The assumed probability model(s) have a significant impact on the efficiency of the procedures used in statistical research.Forthisreason, much work has been devotedtoderivingalargeclass of normal probability distributions andrelated statistical techniques. However,real-worlddatachallenge all established probability models, leaving manyimportant issues unresolved.This present work add another novel distribution with two parameter called two-parameter betaexponential distribution (TPBED), including the beta (2,b)distribution and the new XLindley distribution as special cases. We provide a complete mathematical treatment of this distribution. We derive the moment generating function and the r-th moment, thereby generalizing some results from the literature. Expressions for the density, moment generating function, entropy and the r-th moment of the order statisticare also obtained. We observe in three applications to simulated and real data sets(demography and geostandards) that this model is quite flexible and can be used quite effectively for analyzing active data in place of one and two-parameter distributions such asthe exponential, Lindley, XLindley, new XLindley, Xgamma, Zeghdoudi, Chen, Lindley gamma, quasinew Lindley, two-parameter Lindley, Power XLindley, and Gamma. [ABSTRACT FROM AUTHOR]