Stochastic and Statistical Analysis in Natural Sciences

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

Deadline for manuscript submissions: 28 November 2024 | Viewed by 6211

Special Issue Editors


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Guest Editor
Department of Mathematics, Faculty of Sciences and Mathematics, University of Pristina, Kosovska Mitrovica, Serbia
Interests: stochastic analysis; stochastic calculus; granger causality; causality; brownian motion; stochastic differential equations

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Guest Editor
Department of Informatics and Computer Sciences, University of Criminal Investigation and Police Studies, Cara Dušana Street 196, Belgrade, Serbia
Interests: statistics; probability theory; time series analysis; data analytics; applied mathematics; computing in mathematics and natural science

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Guest Editor
Department of Geospatial and Environmental Science, Faculty of Geography, University of Belgrade, Studenstki Trg 3/III, 11000 Belgrade, Serbia
Interests: GIS; remote sensing; water science; meteorology; climatology; environment; digital cartography; atmosphere; statistics; numerical analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues, 

In stochastic analysis, a stochastic processes (and time series as their special form) is a mathematical object defined as a family of random variables. Examples of such processes include the Brownian motion process used to study price changes, Poisson processes used to study the number of phone calls occurring in a certain period of time, and many others. Stochastic processes are widely used as mathematical models of systems and phenomena which randomly vary with applications in many disciplines such as biology, chemistry, ecology, physics, computer theory, neuroscience, geosciences, medicine, etc. Important aspects of the stochastic analysis of stochastic processes include stochastic integration and stochastic differential equations. In the statistical analysis of stochastic processes, some of the most important considerations are related to parameter estimation, testing the stochastic distributions and stationarity, etc. Geo-statistical methods in geoscience are important for multiple calculations and the analysis of natural phenomena. 

This Special Issue aims to bring together contributions concerning the stochastic and statistical analysis of stochastic processes and time series, both of theoretical and applicative domains. Toward that aim, novel methodologies or applications in natural sciences are welcome, but papers addressing other relevant topics are also invited. 

This Special Issue welcomes submissions concerning research areas including, but not limited to, the following :

  • Stochastic analysis;
  • Conditional measures and expectations;
  • Statistical analysis;
  • Statistical regression analysis in natural sciences;
  • Statistical testing and significance;
  • Stochastic processes with applications in natural sciences;
  • Stochastic differential equations with application in natural sciences;
  • Time-series analysis with application in natural sciences;
  • Statistical methods in the natural sciences;
  • Statistical methods in cross-sectional studies.

Dr. Dragana Valjarević
Prof. Dr. Vladica Stojanović
Dr. Aleksandar Dj Valjarević
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. 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

  • stochastic processes
  • time-series analysis
  • conditional expectation
  • filtration
  • statistical methods in the natural sciences
  • parameter estimation techniques
  • cross-sectional studies
  • population and sample theory

Published Papers (7 papers)

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Research

21 pages, 2294 KiB  
Article
Statistical Advancement of a Flexible Unitary Distribution and Its Applications
by Hugo S. Salinas, Hassan S. Bakouch, Fatimah E. Almuhayfith, Wilson E. Caimanque, Leonardo Barrios-Blanco and Olayan Albalawi
Axioms 2024, 13(6), 397; https://doi.org/10.3390/axioms13060397 - 14 Jun 2024
Viewed by 232
Abstract
A flexible distribution has been introduced to handle random variables in the unit interval. This distribution is based on an exponential transformation of the truncated positive normal distribution with two parameters and can effectively fit data with varying degrees of skewness and kurtosis. [...] Read more.
A flexible distribution has been introduced to handle random variables in the unit interval. This distribution is based on an exponential transformation of the truncated positive normal distribution with two parameters and can effectively fit data with varying degrees of skewness and kurtosis. Therefore, it presents an alternative for modeling this type of data. Several mathematical and statistical properties of this distribution have been derived, such as moments, hazard function, the Bonferroni curve, and entropy. Moreover, we investigate the characterizations of the proposed distribution based on its hazard function. Parameter estimation has been performed using both the maximum likelihood method and method of the moments. Because of this, we were able to determine the best critical region and the information matrix, facilitating the calculation of asymptotic confidence intervals. A simulation study is presented to analyze the behavior of the obtained estimators for different sample sizes. To demonstrate the suitability of the proposed distribution, applications and goodness-of-fit tests have been performed on two practical data sets. Full article
(This article belongs to the Special Issue Stochastic and Statistical Analysis in Natural Sciences)
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17 pages, 383 KiB  
Article
The Measurement Errors and Their Effects on the Cumulative Sum Schemes for Monitoring the Ratio of Two Correlated Normal Variables
by Wei Yang, Xueting Ji and Jiujun Zhang
Axioms 2024, 13(6), 393; https://doi.org/10.3390/axioms13060393 - 12 Jun 2024
Viewed by 199
Abstract
Monitoring the ratio of two correlated normal random variables is often used in many industrial manufacturing processes. At the same time, measurement errors inevitably exist in most processes, which have different effects on the performance of various charting schemes. This paper comprehensively analyses [...] Read more.
Monitoring the ratio of two correlated normal random variables is often used in many industrial manufacturing processes. At the same time, measurement errors inevitably exist in most processes, which have different effects on the performance of various charting schemes. This paper comprehensively analyses the impacts of measurement errors on the detection ability of the cumulative sum (CUSUM) charting schemes for the ratio of two correlated normal variables. A thorough numerical assessment is performed using the Monte Carlo simulation, and the results indicate that the measurement errors negatively impact the performance of the CUSUM scheme for the ratio of two correlated normal variables. Increasing the number of measurements per set is not a lucrative approach for minimizing the negative impact of measurement errors on the performance of the CUSUM charting scheme when monitoring the ratio of two correlated normal variables. We consider a food formulation as an example that illustrates the quality control problems involving the ratio of two correlated normal variables in an industry with a measurement error. The results are presented, along with some suggestions for further study. Full article
(This article belongs to the Special Issue Stochastic and Statistical Analysis in Natural Sciences)
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10 pages, 285 KiB  
Article
Application of the Concept of Statistical Causality in Integrable Increasing Processes and Measures
by Dragana Valjarević, Vladica Stojanović and Aleksandar Valjarević
Axioms 2024, 13(2), 124; https://doi.org/10.3390/axioms13020124 - 17 Feb 2024
Viewed by 769
Abstract
In this paper, we investigate an application of the statistical concept of causality, based on Granger’s definition of causality, on raw increasing processes as well as on optional and predictable measures. A raw increasing process is optional (predictable) if the bounded (left-continuous) process [...] Read more.
In this paper, we investigate an application of the statistical concept of causality, based on Granger’s definition of causality, on raw increasing processes as well as on optional and predictable measures. A raw increasing process is optional (predictable) if the bounded (left-continuous) process X, associated with the measure μA(X), is self-caused. Also, the measure μA(X) is optional (predictable) if an associated process X is self-caused with some additional assumptions. Some of the obtained results, in terms of self-causality, can be directly applied to defining conditions for an optional stopping time to become predictable. Full article
(This article belongs to the Special Issue Stochastic and Statistical Analysis in Natural Sciences)
25 pages, 835 KiB  
Article
Integer-Valued Split-BREAK Process with a General Family of Innovations and Application to Accident Count Data Modeling
by Vladica S. Stojanović, Hassan S. Bakouch, Zorica Gajtanović, Fatimah E. Almuhayfith and Kristijan Kuk
Axioms 2024, 13(1), 40; https://doi.org/10.3390/axioms13010040 - 7 Jan 2024
Viewed by 1069
Abstract
This paper presents a novel count time-series model, named integer-valued Split-BREAK process of the first order, abbr. INSB(1) model. This process is examined in terms of its basic stochastic properties, such as stationarity, mean, variance and correlation structure. In addition, the marginal distribution, [...] Read more.
This paper presents a novel count time-series model, named integer-valued Split-BREAK process of the first order, abbr. INSB(1) model. This process is examined in terms of its basic stochastic properties, such as stationarity, mean, variance and correlation structure. In addition, the marginal distribution, over-dispersion and zero-inflation properties of the INSB(1) process are also examined. To estimate the unknown parameters of the INSB(1) process, an estimation procedure based on probability generating functions (PGFs) is proposed. For the obtained estimators, their asymptotic properties, as well as the appropriate simulation study, are examined. Finally, the INSB(1) process is applied in the dynamic analysis of some real-world series, namely, the numbers of serious traffic accidents in Serbia and forest fires in Greece. Full article
(This article belongs to the Special Issue Stochastic and Statistical Analysis in Natural Sciences)
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16 pages, 480 KiB  
Article
Higher-Order INAR Model Based on a Flexible Innovation and Application to COVID-19 and Gold Particles Data
by Fatimah E. Almuhayfith, Anuresha Krishna, Radhakumari Maya, Muhammad Rasheed Irshad, Hassan S. Bakouch and Munirah Almulhim
Axioms 2024, 13(1), 32; https://doi.org/10.3390/axioms13010032 - 31 Dec 2023
Viewed by 1247
Abstract
INAR models have the great advantage of being able to capture the conditional distribution of a count time series based on their past observations, thus allowing it to be tailored to meet the unique characteristics of count data. This paper reviews the two-parameter [...] Read more.
INAR models have the great advantage of being able to capture the conditional distribution of a count time series based on their past observations, thus allowing it to be tailored to meet the unique characteristics of count data. This paper reviews the two-parameter Poisson extended exponential (PEE) distribution and its corresponding INAR(1) process. Then the INAR of order p (INAR(p)) model that incorporates PEE innovations is proposed, its statistical properties are presented, and its parameters are estimated using conditional least squares and conditional maximum likelihood estimation methods. Two practical data sets are analyzed and compared with competing INAR models in an effort to gauge the performance of the proposed model. It is found that the proposed model performs better than the competitors. Full article
(This article belongs to the Special Issue Stochastic and Statistical Analysis in Natural Sciences)
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16 pages, 4693 KiB  
Article
An Enhanced Spatial Capture Model for Population Analysis Using Unidentified Counts through Camera Encounters
by Mohamed Jaber, Farag Hamad, Robert D. Breininger and Nezamoddin N. Kachouie
Axioms 2023, 12(12), 1094; https://doi.org/10.3390/axioms12121094 - 29 Nov 2023
Viewed by 839
Abstract
Spatial capture models are broadly used for population analysis in ecological statistics. Spatial capture models for unidentified individuals rely on data augmentation to create a zero-inflated population. The unknown true population size can be considered as the number of successes of a binomial [...] Read more.
Spatial capture models are broadly used for population analysis in ecological statistics. Spatial capture models for unidentified individuals rely on data augmentation to create a zero-inflated population. The unknown true population size can be considered as the number of successes of a binomial distribution with an unknown number of independent trials and an unknown probability of success. Augmented population size is a realization of the unknown number of trials and is recommended to be much larger than the unknown population size. As a result, the probability of success of binomial distribution, i.e., the unknown probability that a hypothetical individual in the augmented population belongs to the true population, can be obtained by dividing the unknown true population size by the augmented population size. This is an inverse problem as neither the true population size nor the probability of success is known, and the accuracy of their estimates strongly relies on the augmented population size. Therefore, the estimated population size in spatial capture models is very sensitive to the size of a zero-inflated population and in turn to the estimated probability of success. This is an important issue in spatial capture models as a typical count model with censored data (unidentified and/or undetected). Hence, in this research, we investigated the sensitivity and accuracy of the spatial capture model to address this problem with the objective of improving the robustness of the model. We demonstrated that the estimated population size using the proposed enhanced capture model was more accurate in comparison with the previous spatial capture model. Full article
(This article belongs to the Special Issue Stochastic and Statistical Analysis in Natural Sciences)
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26 pages, 13370 KiB  
Article
Statistical Analysis of Type-II Generalized Progressively Hybrid Alpha-PIE Censored Data and Applications in Electronic Tubes and Vinyl Chloride
by Ahmed Elshahhat, Osama E. Abo-Kasem and Heba S. Mohammed
Axioms 2023, 12(6), 601; https://doi.org/10.3390/axioms12060601 - 16 Jun 2023
Cited by 2 | Viewed by 894
Abstract
A new Type-II generalized progressively hybrid censoring strategy, in which the experiment is ensured to stop at a specified time, is explored when the lifetime model of the test subjects follows a two-parameter alpha-power inverted exponential (Alpha-PIE) distribution. Alpha-PIE’s parameters and reliability indices, [...] Read more.
A new Type-II generalized progressively hybrid censoring strategy, in which the experiment is ensured to stop at a specified time, is explored when the lifetime model of the test subjects follows a two-parameter alpha-power inverted exponential (Alpha-PIE) distribution. Alpha-PIE’s parameters and reliability indices, such as reliability and hazard rate functions, are estimated via maximum likelihood and Bayes estimation methodologies in the presence of the proposed censored data. The estimated confidence intervals of the unknown quantities are created using the normal approximation of the acquired classical estimators. The Bayesian estimators are also produced using independent gamma density priors under symmetrical (squared-error) loss. The Bayes’ estimators and their associated highest posterior density intervals cannot be calculated theoretically since the joint likelihood function is derived in a complicated form, but they can potentially be assessed using Monte Carlo Markov-chain algorithms. We next go through four optimality criteria for identifying the best progressive design. The effectiveness of the suggested estimation procedures is assessed using Monte Carlo comparisons, and certain recommendations are offered. Ultimately, two different applications, one focused on the failure times of electronic tubes and the other on vinyl chloride, are analyzed to illustrate the effectiveness of the proposed techniques that may be employed in real-world scenarios. Full article
(This article belongs to the Special Issue Stochastic and Statistical Analysis in Natural Sciences)
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