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Axioms
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Mathematical Tools and Techniques Applicable to Probability Theory and Statistics...
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Special Issue "Mathematical Tools and Techniques Applicable to Probability Theory and Statistics II"

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 30 December 2023 | Viewed by 3340

Special Issue Editor

Prof. Dr. Hari Mohan Srivastava

grade E-Mail Website
Guest Editor
Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
Interests: real and complex analysis; fractional calculus and its applications; integral equations and transforms; higher transcendental functions and their applications; q-series and q-polynomials; analytic number theory; analytic and geometric Inequalities; probability and statistics; inventory modelling and optimization
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This issue is a continuation of the previous successful Special Issue entitled “Mathematical Tools and Techniques Applicable to Probability Theory and Statistics”. Investigations involving the theory and applications of mathematical analytic tools and techniques are remarkably widespread in many diverse areas of the mathematical, physical, biological, chemical, engineering, and statistical sciences. In this Special Issue, we invite and welcome review, expository, and original research articles dealing with (but not limited to) the recent advances in the subject of (among other related areas) probability theory and statistics.

We are looking forward to your contribution to this Special Issue.

Prof. Dr. Hari Mohan Srivastava
Guest Editor

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. Axioms is an international peer-reviewed open access monthly 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 2400 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

  • mathematical (or higher transcendental) functions and their applications in probability theory and statistics
  • probabilistic derivations and applications of generating functions
  • the notion of statistical convergence and related developments
  • stochastic and martingale sequences and associated approximation theorems
  • statistical inference, statistical mechanics and related areas
  • summability theory and statistical applications

Published Papers (4 papers)

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Article
Bivariate Discrete Odd Generalized Exponential Generator of Distributions for Count Data: Copula Technique, Mathematical Theory, and Applications
by
Laila A. Al-Essa
,
Mohamed S. Eliwa
,
Hend S. Shahen
,
Amal A. Khalil
,
Hana N. Alqifari
and
Mahmoud El-Morshedy
Axioms 2023, 12(6), 534; https://doi.org/10.3390/axioms12060534 - 29 May 2023
Viewed by 454
Abstract
In this article, a new family of bivariate discrete distributions is proposed based on the copula concept, in the so-called bivariate discrete odd generalized exponential-G family. Some distributional properties, including the joint probability mass function, joint survival function, joint failure rate function, median [...] Read more.
In this article, a new family of bivariate discrete distributions is proposed based on the copula concept, in the so-called bivariate discrete odd generalized exponential-G family. Some distributional properties, including the joint probability mass function, joint survival function, joint failure rate function, median correlation coefficient, and conditional expectation, are derived. After proposing the general class, one special model of the new bivariate family is discussed in detail. The maximum likelihood approach is utilized to estimate the family parameters. A detailed simulation study is carried out to examine the bias and mean square error of maximum likelihood estimators. Finally, the importance of the new bivariate family is explained by means of two distinctive real data sets in various fields. Full article
(This article belongs to the Special Issue Mathematical Tools and Techniques Applicable to Probability Theory and Statistics II)
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Article
Consistency of the Estimator for the Common Mean in Fixed-Effect Meta-Analyses
by
Nanami Taketomi
and
Takeshi Emura
Axioms 2023, 12(5), 503; https://doi.org/10.3390/axioms12050503 - 21 May 2023
Viewed by 677
Abstract
Fixed-effect meta-analyses aim to estimate the common mean parameter by the best linear unbiased estimator. Besides unbiasedness, consistency is one of the most fundamental requirements for the common mean estimator to be valid. However, conditions for the consistency of the common mean estimator [...] Read more.
Fixed-effect meta-analyses aim to estimate the common mean parameter by the best linear unbiased estimator. Besides unbiasedness, consistency is one of the most fundamental requirements for the common mean estimator to be valid. However, conditions for the consistency of the common mean estimator have not been discussed in the literature. This article fills this gap by clarifying conditions for making the common mean estimator consistent in fixed-effect meta-analyses. In this article, five theorems are devised, which state regularity conditions for the common mean estimator to be consistent. These theorems are novel applications of the classical large sample theory to meta-analyses. Numerical illustrations are also given to help understand the needs of the regularity conditions. Three real datasets illustrate the practical consequences of the devised theorems. This article concludes that the inconsistency of the common mean estimator occurs under some conditions in real meta-analyses. Full article
(This article belongs to the Special Issue Mathematical Tools and Techniques Applicable to Probability Theory and Statistics II)
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Article
Bayesian Inference and Data Analysis of the Unit–Power Burr X Distribution
by
Aisha Fayomi
,
Amal S. Hassan
,
Hanan Baaqeel
and
Ehab M. Almetwally
Axioms 2023, 12(3), 297; https://doi.org/10.3390/axioms12030297 - 14 Mar 2023
Cited by 4 | Viewed by 641
Abstract
The unit–power Burr X distribution (UPBXD), a bounded version of the power Burr X distribution, is presented. The UPBXD is produced through the inverse exponential transformation of the power Burr X distribution, which is also beneficial for modelling data on the unit interval. [...] Read more.
The unit–power Burr X distribution (UPBXD), a bounded version of the power Burr X distribution, is presented. The UPBXD is produced through the inverse exponential transformation of the power Burr X distribution, which is also beneficial for modelling data on the unit interval. Comprehensive analysis of its key characteristics is performed, including shape analysis of the primary functions, analytical expression for moments, quantile function, incomplete moments, stochastic ordering, and stress–strength reliability. Rényi, Havrda and Charvat, and d-generalized entropies, which are measures of uncertainty, are also obtained. The model’s parameters are estimated using a Bayesian estimation approach via symmetric and asymmetric loss functions. The Bayesian credible intervals are constructed based on the marginal posterior distribution. Monte Carlo simulation research is intended to test the accuracy of various estimators based on certain measures, in accordance with the complex forms of Bayesian estimators. Finally, we show that the new distribution is more appropriate than certain other competing models, according to their application for COVID-19 in Saudi Arabia and the United Kingdom. Full article
(This article belongs to the Special Issue Mathematical Tools and Techniques Applicable to Probability Theory and Statistics II)
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Article
Different Estimation Methods for New Probability Distribution Approach Based on Environmental and Medical Data
by
Eid A. A. Hassan
,
Mohammed Elgarhy
,
Eman A. Eldessouky
,
Osama H. Mahmoud Hassan
,
Essam A. Amin
and
Ehab M. Almetwally
Axioms 2023, 12(2), 220; https://doi.org/10.3390/axioms12020220 - 20 Feb 2023
Cited by 1 | Viewed by 994
Abstract
In this article, we introduce a new extension of the power Lomax (PLo) model by combining the type II exponentiated half-logistic class of statistical models and the PLo model. The new suggested statistical model called type II exponentiated half-logistic-PLo (TIIEHL-PLo) model. However, the [...] Read more.
In this article, we introduce a new extension of the power Lomax (PLo) model by combining the type II exponentiated half-logistic class of statistical models and the PLo model. The new suggested statistical model called type II exponentiated half-logistic-PLo (TIIEHL-PLo) model. However, the new TIIEHL-PLo model is more flexible and applicable than the PLo model and some extensions of THE PLo model, especially those in environmental and medical fields. Some general statistical properties of the TIIEHL-PLo model are computed. Six different estimation approaches, namely maximum likelihood (ML), least-square (LS), weighted least-squares (WLS), maximum product spacing (MPS), Cramér–von Mises (CVM), and Anderson–Darling (AD) estimation approaches, are utilized to estimate the parameters of the TIIEHL-PLo model. The simulation experiment examines the accuracy of the model parameters by employing six different methodologies of estimation. In this study, we analyze three real datasets from the environmental and medical fields to highlight the relevance and adaptability of the proposed approach. The newly suggested model is exceptionally adaptable and outperforms several well-known statistical models. Full article
(This article belongs to the Special Issue Mathematical Tools and Techniques Applicable to Probability Theory and Statistics II)
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