Articles
Publication Date: 2026
Aut Journal Of Mathematics And Computing (27832449)7(1)pp. 1-18
In this paper, some general classes of bivariate semi-parametric continuous distributions are introduced. Some important properties of this family of distributions will be illustrated. It is seen that the bivariate distribution corresponds to the known Ali-Mikhail-Haq copula. Hence, some important properties such as the TP2 property are justified. It will be shown that the marginals are kind of heavy tailed weighted distributions whose hazard rate functions can take variety of shapes. The behavior of the hazard rate function is mathematically illustrated. In addition, the α-power transformed distributions of a second type, which are introduced for the first time here, can be verified as special cases of the marginals. Some members of the new bivariate classes are studied in details. The estimation of the parameters is illustrated by means of an efficient expectation-maximization algorithm, and some real data sets are also analyzed for illustrative purposes. © 2026 The Author(s).
Publication Date: 2025
Journal of Statistical Theory and Practice (15598616)19(2)
In this paper, another motivation for the well-known quadratic transmuted family of distributions is pointed out and a new relation for the expected value of this family in terms of the Gini index is presented. A bug of the generalized transmuted-G family of distributions Nofal et al. (Commun Stat Theory Methods 46:4119–4136, 2016) is illustrated. In that work, the necessary conditions for the density and distribution functions are not satisfied, for some parameter values. Moreover, a new flexible family of distributions is introduced from a fresh perspective, and their key properties are studied in general forms. As an example, a new high flexible distribution is introduced and some of its important futures such as the moment generating function, moments, order statistics and the stress-strength parameter are investigated. In addition, the parameters of the proposed new distribution are estimated using the maximum likelihood method, and three real data sets are scrutinized to assess the distribution’s adequacy in providing satisfactory fits. © Grace Scientific Publishing 2025.
Publication Date: 2024
Journal Of The Iranian Statistical Society (17264057)23(1)pp. 99-115
This paper examines a novel extension of the geometric distribution characterized by two parameters, that is not created based on discretizing existing continuous models. This model, due to its analytical form of the cumulative distribution function and simple structure, can be of interest from mathematical perspectives, particularly in cases where the analysis of stochastic orders is desired. In addition, it is a suitable candidate for analyzing monotone hazard rate discrete data, in view of the fact that its hazard rate function exhibits monotonicity in both increasing and decreasing directions. Additionally, the behavior of the survival function of residual lifetime is briefly addressed. The parameters of the distribution are estimated using the maximum likelihood method, and a real-world data set is scrutinized to assess the distribution's adequacy in providing satisfactory fits. © (2024), (Iranian Statistical Society). All rights reserved.
Publication Date: 2021
Journal of Applied Statistics (02664763)48(6)pp. 1071-1090
In this paper, a new bivariate discrete generalized exponential distribution, whose marginals are discrete generalized exponential distributions, is studied. It is observed that the proposed bivariate distribution is a flexible distribution whose cumulative distribution function has an analytical structure. In addition, a new bivariate geometric distribution can be obtained as a special case. We study different properties of this distribution and propose estimation of its parameters. We will see that the maximum of the variables involved in the proposed bivariate distribution defines some new classes of univariate discrete distributions, which are interesting in their own sake, and can be used to analyze some Reliability systems whose components are positive dependent. Some important futures of this new univariate family of discrete distributions are also studied in details. In addition, a general class of bivariate discrete distributions, whose marginals are exponentiated discrete distributions, is introduced. Moreover, the analysis of two real bivariate data sets is performed to indicate the effectiveness of the proposed models. Finally, we conclude the paper. © 2020 Informa UK Limited, trading as Taylor & Francis Group.
