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This article presents a new class of generalized transmuted lifetime distributions which includes a large number of lifetime distributions as sub-family. Several important mathematical quantities such as density function, distribution…
We introduce the beta generalized exponential distribution that includes the beta exponential and generalized exponential distributions as special cases. We provide a comprehensive mathematical treatment of this distribution. We derive the…
In this paper, we introduce a new class of bivariate distributions by compounding the bivariate generalized exponential and power-series distributions. This new class contains some new sub-models such as the bivariate generalized…
This article aims to introduced a new distribution named as extended xgamma (EXg) distribution. This generalization is derived from xgamma distribution (Xg), a special finite mixture of exponential and gamma distributions [see, Sen et al.…
Many multivariate statistical analysis methods and their corresponding probabilistic counterparts have been adopted to develop process monitoring models in recent decades. However, the insightful connections between them have rarely been…
A new class of distributions, called Generalized One Parameter Polynomial Exponential-G family of distributions is proposed for modelling lifetime data. An account of the structural and reliability properties of the new class is presented.…
Exponential distributions appear in a wide range of applications including chemistry, nuclear physics, time series analyses, and stock market trends. There are conceivable circumstances in which one would be interested in the cumulative…
This article aims to introduced a new lifetime distribution named as exponentiated xgamma distribution (EXGD). The new generalization obtained from xgamma distribution, a special finite mixture of exponential and gamma distributions. The…
Understanding how well a deep generative model captures a distribution of high-dimensional data remains an important open challenge. It is especially difficult for certain model classes, such as Generative Adversarial Networks and Diffusion…
In numerous instances, the generalized exponential distribution can be used as an alternative to the most widely used non-regular family of distributions: Weibull, gamma, lognormal with three-parameters when analyzing lifetime or any skewed…
Recently, Verma et al. (2025) introduced a novel generalized class of Kavya-Manoharan distributions, which have demonstrated significant utility in reliability analysis and the modeling of lifetime data. This paper proposes an extension of…
The Gumbel model is a very popular statistical model due to its wide applicability for instance in the course of certain survival, environmental, financial or reliability studies. In this work, we have introduced a bimodal generalization of…
A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…
This text presents an unified approach of probability and statistics in the pursuit of understanding and computation of randomness in engineering or physical or social system with prediction with generalizability. Starting from elementary…
We study model evaluation and model selection from the perspective of generalization ability (GA): the ability of a model to predict outcomes in new samples from the same population. We believe that GA is one way formally to address…
Marshall and Olkin (1997, Biometrika, 84, 641 - 652) introduced a very powerful method to introduce an additional parameter to a class of continuous distribution functions and hence it brings more flexibility to the model. They have…
Exponential random graph models (ERGMs) are a widely used framework for network data, enabling hypothesis testing on the structural mechanisms underlying observed networks. Bayesian ERGMs provide principled uncertainty quantification and…
The distribution of the sum of dependent risks is a crucial aspect in actuarial sciences, risk management and in many branches of applied probability. In this paper, we obtain analytic expressions for the probability density function (pdf)…
From the integration of non-symmetrical hyperboles, a one-parameter generalization of the logarithmic function is obtained. Inverting this function, one obtains the generalized exponential function. We show that functions characterizing…
In this paper, we propose a new class of distributions by exponentiating the random variables associated with the probability density functions of composite distributions. We also derive some mathematical properties of this new class of…