A new method for generating distributions with an application to exponential distribution

Abstract

A new method has been proposed to introduce an extra parameter to a family of distributions for more flexibility. A special case has been considered in details namely; one parameter exponential distribution. Various properties of the proposed distribution, including explicit expressions for the moments, quantiles, mode, moment generating function, mean residual lifetime, stochastic orders, order statistics and expression of the entropies are derived. The maximum likelihood estimators of unknown parameters cannot be obtained in explicit forms, and they have to be obtained by solving non-linear equations only. Further we consider an extension of the two-parameter exponential distribution also, mainly for data analysis purposes.Two data sets have been analyzed to show how the proposed models work in practice.

A modified T-X family of distributions: classical and Bayesian analysis

“…In persuasion, Alzaatreh et al [10] proposed an operator namely T-X family, capable of generating the mentioned families of distributions under certain specifications. For more recent development, one may see Alizadeh et al [11], Nofal et al [12], Cordeiro et al [13], Mahdavi and Kundu [14], Haq et al [15] and Basheer [16], among others. In this article, we focus on proposing a new family of distributions, namely modified T-X family of distributions.…”

Alpha power transformed extended exponential distribution: properties and applications

“…Recently, alpha power transformation (APT) has been proposed by Mahdavi and Kundu [15] in order to get more flexibility to a family of distributions. The cdf of a continuous random variable X has APT family is defined as follows:…”

“…In view of the APT, we explore the APTEE model from the EE distribution. The APTEE distribution contains special recent models, namely; APT exponential (Mahdavi and Kundu [15]) and APT Lindley (Dey et al [6]). At the same time, it contains special classical distributions which are exponential, Lindley and gamma.…”

Alpha Power Transformed Inverse Lomax Distribution with Different Methods of Estimation and Applications

“…Finally, we used three real-life datasets to show the flexibility of the APTIL distribution. − α , x, a, b > 0.(2)Mahdavi and Kundu [8] introduced the alpha power transformation (APT) method to add an additional parameter to a family of distributions to increase flexibility in given family. e cdf and pdf of APT-G family are Hindawi Complexity Volume 2020, Article ID 1860813, 15 pages https://doi.…”