Special Issue Information

Dear Colleagues,

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

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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 quarterly 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 1400 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

Related Special Issue

Published Papers (2 papers)

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Research

Open AccessArticle

A Method for Visualizing Posterior Probit Model Uncertainty in the Early Prediction of Fraud for Sustainability Development

Shih-Hsien Tseng

and

Tien Son Nguyen

Axioms 2021, 10(3), 178; https://doi.org/10.3390/axioms10030178 - 04 Aug 2021

Viewed by 349

Abstract

Corporate fraud is not only curtailed investors’ rights and privileges but also disrupts the overall market economy. For this reason, the formulation of a model that could help detect any unusual market fluctuations would be essential for investors. Thus, we propose an early warning system for predicting fraud associated with financial statements based on the Bayesian probit model while examining historical data from 1999 to 2017 with 327 businesses in Taiwan to create a visual method to aid in decision making. In this study, we utilize a parametric estimation via the Markov Chain Monte Carlo (MCMC). The result show that it can reduce over or under-confidence within the decision-making process when standard logistic regression is utilized. In addition, the Bayesian probit model in this study is found to offer more accurate calculations and not only represent the prediction value of the responses but also possible ranges of these responses via a simple plot. Full article

(This article belongs to the Special Issue Mathematical Tools and Techniques Applicable to Probability Theory and Statistics)

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Open AccessArticle

Water Particles Monitoring in the Atacama Desert: SPC Approach Based on Proportional Data

Anderson Fonseca

Paulo Henrique Ferreira

Diego Carvalho do Nascimento

Rosemeire Fiaccone

Christopher Ulloa-Correa

Ayón García-Piña

and

Francisco Louzada

Axioms 2021, 10(3), 154; https://doi.org/10.3390/axioms10030154 - 13 Jul 2021

Viewed by 686

Abstract

Statistical monitoring tools are well established in the literature, creating organizational cultures such as Six Sigma or Total Quality Management. Nevertheless, most of this literature is based on the normality assumption, e.g., based on the law of large numbers, and brings limitations towards truncated processes as open questions in this field. This work was motivated by the register of elements related to the water particles monitoring (relative humidity), an important source of moisture for the Copiapó watershed, and the Atacama region of Chile (the Atacama Desert), and presenting high asymmetry for rates and proportions data. This paper proposes a new control chart for interval data about rates and proportions (symbolic interval data) when they are not results of a Bernoulli process. The unit-Lindley distribution has many interesting properties, such as having only one parameter, from which we develop the unit-Lindley chart for both classical and symbolic data. The performance of the proposed control chart is analyzed using the average run length (ARL), median run length (MRL), and standard deviation of the run length (SDRL) metrics calculated through an extensive Monte Carlo simulation study. Results from the real data applications reveal the tool’s potential to be adopted to estimate the control limits in a Statistical Process Control (SPC) framework. Full article

(This article belongs to the Special Issue Mathematical Tools and Techniques Applicable to Probability Theory and Statistics)

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