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New Advances in Distribution Theory and Its Applications
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New Advances in Distribution Theory and Its Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Probability and Statistics".

Deadline for manuscript submissions: 15 April 2025 | Viewed by 11638

Special Issue Editors

Prof. Dr. Domma Filippo

E-Mail Website
Guest Editor
Department of Economics, Statistics and Finance, University of Calabria, 87036 Arcavacata, Italy
Interests: distribution theory; copula function; inference; income distribution; stochastic frontier analysis
Special Issues, Collections and Topics in MDPI journals
Dr. Francesca Condino

E-Mail Website
Guest Editor
Department of Economics, Statistics and Finance, University of Calabria, 87036 Arcavacata, Italy
Interests: statistics; parametric inference; distribution functions; survival analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In recent years, the field of research relating to distribution theory has weakened due to the countless proposals for “new” distributions, which, in many cases, are now built with standardized techniques, paying particular attention to elegance and mathematical rigor at the cost of greater complexity, which reduces the interpretability, for example, of parameters, without guaranteeing great flexibility with respect to the distributions already present in the literature.  

The purpose of this Special Issue is to stimulate researchers to propose high-quality original articles that provide significant contributions to statistical distribution theory and its applications, with particular attention to the flexibility of models and the interpretability of parameters (or their transformations). In this context, papers suggesting models whose genesis is attributable to specific mechanisms or characteristics related to the context of analysis, general frameworks of families of distribution functions, motivated reparameterizations that increase the interpretability of models, regressive models on characteristics and/or indicators of specific interest, and original applications on real data are welcome.

Prof. Dr. Domma Filippo
Dr. Francesca Condino
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • reparameterization
  • families of distribution functions
  • flexibility
  • unit distribution function
  • income distribution

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Published Papers (8 papers)

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Research

23 pages, 503 KiB  
Article
Mathematical Formalization and Applications to Data with Excess of Zeros and Ones of the Unit-Proportional Hazard Inflated Models
by Guillermo Martínez-Flórez, Roger Tovar-Falón and Héctor W. Gómez
Mathematics 2024, 12(22), 3566; https://doi.org/10.3390/math12223566 - 15 Nov 2024
Viewed by 310
Abstract
In this study, we model the rate or proportion of a specific phenomenon using a set of known covariates. To fit the regression model, which explains the phenomenon within the intervals (0,1), [0,1), [...] Read more.
In this study, we model the rate or proportion of a specific phenomenon using a set of known covariates. To fit the regression model, which explains the phenomenon within the intervals (0,1), [0,1), (0,1], or [0,1], we employ a logit link function. This approach ensures that the model’s predictions remain within the appropriate range of zero to one. In cases of inflation at zero, one, or both, the logit link function is similarly applied to model the dichotomous Bernoulli-type variable with a multinomial response. The findings demonstrate that the model yields a non-singular information matrix, ensuring valid statistical inference. This ensures the invertibility of the information matrix, allowing for hypothesis testing based on likelihood statistics regarding the parameters in the model. This is not possible with other asymmetric models, such as those derived from the skew-normal distribution, which has a singular information matrix at the boundary of the skewness parameter. Finally, empirical results show the model’s effectiveness in analyzing proportion data with inflation at zero and one, proving its robustness and practicality for analyzing bounded data in various fields of research. Full article
(This article belongs to the Special Issue New Advances in Distribution Theory and Its Applications)
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51 pages, 460 KiB  
Article
A Review of Wrapped Distributions for Circular Data
by William Bell and Saralees Nadarajah
Mathematics 2024, 12(16), 2440; https://doi.org/10.3390/math12162440 - 6 Aug 2024
Viewed by 643
Abstract
The wrapped method is the most widely used method for constructing distributions for circular data. In this paper, we provide a review of all known wrapped distributions, including 45 distributions for continuous circular data and 10 distributions for discrete circular data. For each [...] Read more.
The wrapped method is the most widely used method for constructing distributions for circular data. In this paper, we provide a review of all known wrapped distributions, including 45 distributions for continuous circular data and 10 distributions for discrete circular data. For each wrapped distribution, we state its nth trigonometric moment, mean direction, mean resultant length, skewness, and kurtosis. We also discuss data applications and limitations of each wrapped distribution. This review could be a useful reference and encourage the development of more wrapped distributions. We also mention an R package available for fitting all of the reviewed distributions and illustrate its applications. Full article
(This article belongs to the Special Issue New Advances in Distribution Theory and Its Applications)
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16 pages, 2369 KiB  
Article
On Stochastic Representations of the Zero–One-Inflated Poisson Lindley Distribution
by Razik Ridzuan Mohd Tajuddin and Noriszura Ismail
Mathematics 2024, 12(5), 778; https://doi.org/10.3390/math12050778 - 6 Mar 2024
Viewed by 837
Abstract
A zero–one-inflated Poisson Lindley distribution has been introduced recently as an alternative to the zero–one-inflated Poisson distribution for describing count data with a substantial number of zeros and ones. Several stochastic representations of the zero–one-inflated Poisson Lindley distribution and their equivalence to some [...] Read more.
A zero–one-inflated Poisson Lindley distribution has been introduced recently as an alternative to the zero–one-inflated Poisson distribution for describing count data with a substantial number of zeros and ones. Several stochastic representations of the zero–one-inflated Poisson Lindley distribution and their equivalence to some well-known distributions under some conditions are presented. Using these stochastic representations, the distributional properties such as the nth moments, as well as the conditional distributions are discussed. These stochastic representations can be used to explain the relationship between two or more distributions. Several likelihood ratio tests are developed and examined for the presence of one-inflation and fixed rate parameters. The likelihood ratio tests are found to be powerful and have ability to control the error rates as the sample size increases. A sample size of 1000 is acceptable and sufficient for the likelihood ratio tests to be useful. Full article
(This article belongs to the Special Issue New Advances in Distribution Theory and Its Applications)
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22 pages, 1324 KiB  
Article
Unit Exponential Probability Distribution: Characterization and Applications in Environmental and Engineering Data Modeling
by Hassan S. Bakouch, Tassaddaq Hussain, Marina Tošić, Vladica S. Stojanović and Najla Qarmalah
Mathematics 2023, 11(19), 4207; https://doi.org/10.3390/math11194207 - 9 Oct 2023
Cited by 11 | Viewed by 2029
Abstract
Distributions with bounded support show considerable sparsity over those with unbounded support, despite the fact that there are a number of real-world contexts where observations take values from a bounded range (proportions, percentages, and fractions are typical examples). For proportion modeling, a flexible [...] Read more.
Distributions with bounded support show considerable sparsity over those with unbounded support, despite the fact that there are a number of real-world contexts where observations take values from a bounded range (proportions, percentages, and fractions are typical examples). For proportion modeling, a flexible family of two-parameter distribution functions associated with the exponential distribution is proposed here. The mathematical and statistical properties of the novel distribution are examined, including the quantiles, mode, moments, hazard rate function, and its characterization. The parameter estimation procedure using the maximum likelihood method is carried out, and applications to environmental and engineering data are also considered. To this end, various statistical tests are used, along with some other information criterion indicators to determine how well the model fits the data. The proposed model is found to be the most efficient plan in most cases for the datasets considered. Full article
(This article belongs to the Special Issue New Advances in Distribution Theory and Its Applications)
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24 pages, 903 KiB  
Article
Univariate Probability-G Classes for Scattered Samples under Different Forms of Hazard: Continuous and Discrete Version with Their Inferences Tests
by Mohamed S. Eliwa, Muhammad H. Tahir, Muhammad A. Hussain, Bader Almohaimeed, Afrah Al-Bossly and Mahmoud El-Morshedy
Mathematics 2023, 11(13), 2929; https://doi.org/10.3390/math11132929 - 29 Jun 2023
Viewed by 1021
Abstract
In this paper, we define a new generator to propose continuous as well as discrete families (or classes) of distributions. This generator is used for the DAL model (acronym of the last names of the authors, Dimitrakopoulou, Adamidis, and Loukas). This newly proposed [...] Read more.
In this paper, we define a new generator to propose continuous as well as discrete families (or classes) of distributions. This generator is used for the DAL model (acronym of the last names of the authors, Dimitrakopoulou, Adamidis, and Loukas). This newly proposed family may be called the new odd DAL (NODAL) G-class or alternate odd DAL G-class of distributions. We developed both a continuous as well as discrete version of this new odd DAL G-class. Some mathematical and statistical properties of these new G-classes are listed. The estimation of the parameters is discussed. Some structural properties of two special models of these classes are described. The introduced generators can be effectively applied to discuss and analyze the different forms of failure rates including decreasing, increasing, bathtub, and J-shaped, among others. Moreover, the two generators can be used to discuss asymmetric and symmetric data under different forms of kurtosis. A Monte Carlo simulation study is reported to assess the performance of the maximum likelihood estimators of these new models. Some real-life data sets (air conditioning, flood discharges, kidney cysts) are analyzed to show that these newly proposed models perform better as compared to well-established competitive models. Full article
(This article belongs to the Special Issue New Advances in Distribution Theory and Its Applications)
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25 pages, 1004 KiB  
Article
Unit Distributions: A General Framework, Some Special Cases, and the Regression Unit-Dagum Models
by Francesca Condino and Filippo Domma
Mathematics 2023, 11(13), 2888; https://doi.org/10.3390/math11132888 - 27 Jun 2023
Cited by 2 | Viewed by 1870
Abstract
In this work, we propose a general framework for models with support in the unit interval, which is obtained using the technique of random variable transformations. For this class, the general expressions of distribution and density functions are given, together with the principal [...] Read more.
In this work, we propose a general framework for models with support in the unit interval, which is obtained using the technique of random variable transformations. For this class, the general expressions of distribution and density functions are given, together with the principal characteristics, such as quantiles, moments, and hazard and reverse hazard functions. It is possible to verify that different proposals already present in the literature can be seen as particular cases of this general structure by choosing a suitable transformation. Moreover, we focus on the class of unit-Dagum distributions and, by specifying two different kinds of transformations, we propose the type I and type II unit-Dagum distributions. For these two models, we first consider the possibility of expressing the distribution in terms of indicators of interest, and then, through the regression approach, relate the indicators and covariates. Finally, some applications using data on the unit interval are reported. Full article
(This article belongs to the Special Issue New Advances in Distribution Theory and Its Applications)
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16 pages, 714 KiB  
Article
Zero-Dependent Bivariate Poisson Distribution with Applications
by Najla Qarmalah and Abdulhamid A. Alzaid
Mathematics 2023, 11(5), 1194; https://doi.org/10.3390/math11051194 - 28 Feb 2023
Viewed by 1789
Abstract
The bivariate Poisson model is the most widely used model for bivariate counts, and in recent years, several bivariate Poisson regression models have been developed in order to analyse two response variables that are possibly correlated. In this paper, a particular class of [...] Read more.
The bivariate Poisson model is the most widely used model for bivariate counts, and in recent years, several bivariate Poisson regression models have been developed in order to analyse two response variables that are possibly correlated. In this paper, a particular class of bivariate Poisson model, developed from the bivariate Bernoulli model, will be presented and investigated. The proposed bivariate Poisson models use dependence parameters that can model positively and negatively correlated data, whereas more well-known models, such as Holgate’s bivariate Poisson model, can only be used for positively correlated data. As a result, the proposed model contributes to improving the properties of the more common bivariate Poisson regression models. Furthermore, some of the properties of the new bivariate Poisson model are outlined. The method of maximum likelihood and moment method were used to estimate the parameters of the proposed model. Additionally, real data from the healthcare utilization sector were used. As in the case of healthcare utilization, dependence between the two variables may be positive or negative in order to assess the performance of the proposed model, in comparison to traditional bivariate count models. All computations and graphs shown in this paper were produced using R programming language. Full article
(This article belongs to the Special Issue New Advances in Distribution Theory and Its Applications)
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26 pages, 1847 KiB  
Article
Statistical Inference on a Finite Mixture of Exponentiated Kumaraswamy-G Distributions with Progressive Type II Censoring Using Bladder Cancer Data
by Refah Alotaibi, Lamya A. Baharith, Ehab M. Almetwally, Mervat Khalifa, Indranil Ghosh and Hoda Rezk
Mathematics 2022, 10(15), 2800; https://doi.org/10.3390/math10152800 - 7 Aug 2022
Cited by 2 | Viewed by 1437
Abstract
A new family of distributions called the mixture of the exponentiated Kumaraswamy-G (henceforth, in short, ExpKum-G) class is developed. We consider Weibull distribution as the baseline (G) distribution to propose and study this special sub-model, which we call the exponentiated Kumaraswamy Weibull distribution. [...] Read more.
A new family of distributions called the mixture of the exponentiated Kumaraswamy-G (henceforth, in short, ExpKum-G) class is developed. We consider Weibull distribution as the baseline (G) distribution to propose and study this special sub-model, which we call the exponentiated Kumaraswamy Weibull distribution. Several useful statistical properties of the proposed ExpKum-G distribution are derived. Under the classical paradigm, we consider the maximum likelihood estimation under progressive type II censoring to estimate the model parameters. Under the Bayesian paradigm, independent gamma priors are proposed to estimate the model parameters under progressive type II censored samples, assuming several loss functions. A simulation study is carried out to illustrate the efficiency of the proposed estimation strategies under both classical and Bayesian paradigms, based on progressively type II censoring models. For illustrative purposes, a real data set is considered that exhibits that the proposed model in the new class provides a better fit than other types of finite mixtures of exponentiated Kumaraswamy-type models. Full article
(This article belongs to the Special Issue New Advances in Distribution Theory and Its Applications)
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