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Modeling COVID-19 data with a novel neutrosophic Burr-III distribution

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Thank you for visiting nature. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser or turn off compatibility mode in Internet Explorer. In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript. In this study, we have presented a novel probabilistic model called the neutrosophic Burr-III distribution, designed for applications in neutrosophic surface analysis. Neutrosophic analysis allows for the incorporation of vague and imprecise information, reflecting the reality that many real-world problems involve ambiguous data. This ability to handle vagueness can lead to more robust and realistic models especially in situation where classical models fall short. We have also explored the neutrosophic Burr-III distribution in order to deal with the ambiguity and vagueness in the data where the classical Burr-III distribution falls short. This distribution offers valuable insights into various reliability properties, moment expressions, order statistics, and entropy measures, making it a versatile tool for analyzing complex data. To assess the practical relevance of our proposed distribution, we applied it to real-world data sets and compared its performance against the classical Burr-III distribution. The findings revealed that the neutrosophic Burr-III distribution outperformed than the classical Burr-III distribution in capturing the underlying data characteristics, highlighting its potential as a superior modeling toolin various fields. Historically, in , Burr formulated twelve families of distributions through the Kearl Pearson equation, each offering distinct density functions with diverse applications. Among these, the Burr-III distribution has gained widespread acceptance and recognition. However, the Burr-III distribution has often been overlooked in favor of other Burr family of distributions. Examples of its applications include forestry studies by Gove et al. The Burr-III distribution often referred to as the Dagum distribution in income and earning studies as observed in 9 is significant component in the field of science. In the realm of real-world applications, it is known as the inverse Burr-XIII distribution as highlighted in Benjamin et al. Despite the widespread use of the Burr-III distribution, existing research work has encountered certain limitations with the classical Burr-III distribution as:. One primary challenge is its inability to effectively capture the complexities of real-world datasets characterized by uncertainty and ambiguity. Many complex problems inherently involve vague and imprecise information, which classical Burr-III model often struggle to address adequately. The classical Burr-III model assumed that data is crisp and well-defined, which may not always hold true in practice. This discrepancy between the assumptions of classical Burr-III model and the nature of real-world data introduces a significant source of error and uncertainty in statistical analyses. To address these limitations, there is a growing need for alternative approaches that can accommodate uncertainty and indeterminacy in data analysis. One promising paradigm shift in this regard is the field of neutrosophic analysis, which introduces a novel approach for handling data uncertainty. It encompasses both uncertain data and the methodologies employed to evaluate such data. The distinguishing feature of neutrosophic statistics lies in its ability to accommodate uncertainty and indeterminacy, a departure from classical statistics where all data is crisp and well-defined. Neutrosophic statistics come into play when data contains indeterminacy, offering valuable tools for analyzing such uncertain information. Numerous neutrosophic probability distributions have been developed in the literature, for instance, neutrosophic Weibull distribution by Al-hasan and Smarandache 12 , neutrosophic uniform, neutrosophic exponential and neutrosophic Poisson by Al-habib et al. In this study, we aim to introduce a ground breaking probabilistic model known as the Netrosophic Burr-III NeS-BrIII distribution, specifically designed to tackle the intricacies of neutrosophic surface analysis. Our exploration into the NeS-BrIII distribution delves deep into its capabilities, unveiling its potential to address the challenges posed by ambiguity and vagueness in the data that the classical Burr-III distribution cannot meet these challenges. This unique distribution not only offers insights into reliability properties, moment expressions, order statistics, and entropy measures but also serves as a versatile tool for unraveling the complexities of real-world datasets. To gauge the practical significance of our proposed NeS-BrIII distribution, we applied it to real-world datasets and subject it to rigorous performance evaluation. The structure of the paper is formatted as: Section ' The model with properties ' laid the foundation for the current study by presenting the development of the NeS-BrIII distribution. We delved into its characteristics and conduct simulations to further elucidate its behavior. Through these applications, we showcase how the distribution can be effectively employed to analyze and model real data, offering insights into its performance and versatility. The final section, Section ' Conclusion ', serves as the conclusion of our study by summarizing the key findings, contributions and implications of our research. In this section, we delve into the development of the neutrosophic model based on the classical Burr-III distribution. After model development, the second step involves investigating the properties and characteristics of the NeS-BrIII distribution, including moments, reliability properties, order statistics, and entropy measures. These analyses provide insights into the behavior and performance of the distribution in various contexts. This method leverage neutrospohic statistics to estimate the parameters of the distribution from the observed data. This unimodel nature of the model suggests that the distribution predominantly exhibit a single peak, signifying a concentration of values around a specific point. The NeS-BrIII distribution offers a wealth of properties and computations that significantly enhance the understanding of its practical implementation within distribution theory. Key properties such as moments, percentiles, random number generation, as well as maximum likelihood estimation MLE and dependability measures have been rigorously determined for the NeS-BrIII distribution. These calculated properties and measures collectively contribute to a comprehensive characterization of the NeS-BrIII distribution, enhancing its utility in various theoretical and practical contexts within distribution theory. Moments serve as essential statistical measures that bridge theory and observations. Moments are calculated values that describe key properties of a distribution, specifically the expected values of different powers of the random variable. To apply moments to real-world data, we adjust them to match sample moments. This adjustment process involves equating estimated moments from observed data to their corresponding population moments. The number of equations generated in this process equals the number of parameters being estimated. This coefficient is widely used for analyzing relationships within data is fundamental in statistical analysis. Skewness C 1 and kurtosis C 2 can be computed from the following moment ratios:. Table 1 provides a comprehensive overview of computed statistical first four moments, variance V , skewness C 1 and kurtosis C 2 for the some arbitrary parametric values of NeS-BrIII distribution using R-Programming language. In general the quantile function QF is a mathematical expression used to determine specific quantiles of the distribution. In the realm of probability distribution, a distribution function typically adheres to two important characteristics: it is a non-decreasing function, and its QF is left-continuous. The QF maps values from the range \[0, 1\], representing the probabilities. When we set the quantile value to 0. The median is a crucial measure that divides the distribution into two equal halves, making it an essential indicator of central tendency in this particular distribution. Reliability is often defined as a device's capacity to work under a specific set of circumstances until it fails. Strength that can withstand stress under constant operating conditions is included into several of the devices' designs. The link between stress and strength is complex. Engineering, medicine, sociology, and other fields of study have all examined it. This, nevertheless, the 'stress-strength' or 'reliability' models are a collection of probabilistic models. When the component is subjected to stress that exceeds its strength, it will fail, but it will still work properly. Then fromEquations 3 and 4 , we have. Order statistics are essential in data analysis and their features. Statistical implementations have been extensively researched in the literature. The oldest model for ordered random variables is probably order statistics. When observations in a sample are ordered in increasing order of size, order statistics emerge naturally in life. Order statistics is also useful for studying distribution of maximum, minimum and median etc. An entropy is a numerical measure of a system's uncertainties. The higher the entropy, the more unpredictable the data. The entropy of Renyi is defined as:. From Eq. MLE is a fundamental statistical method used to estimate the parameters of a statistical model by maximizing the likelihood function. MLE provides efficient and asymptotically unbiased estimates, and its widespread use in various fields underscores its importance as a robust and consistent method for parameter estimation. In this section, we carried out a simulation study to check the behavior of proposed estimators for the NeS-BrIII model. The average estimates AEs , biases and mean square error MSEs are computed to check the performance of the best estimator as:. The results of the simulation study are listed in Tables 2 , 3 and 4. The results given in the Tables 2 , 3 and 4 showed that MLEs are consistent estimators. The biases and MSEs decreased by increased in the sample size. An application on two actual data setsis being presented in this section. We have converted the classical data into neutrosophic form to deal with the imprecision, uncertainty or ambiguity in the classical data. The lower values represent the classical statistics and the upper values represent the neutrosophic statistics in the interval form of the data. This data had been formed of rough mortality rate taken from Almongy et al. Advancements and perspectives in COVID research are essential for addressing the multifaceted challenges posed by the pandemic, protecting public health, and building a more resilient and prepared society for the future. Recent studies have highlighted innovative computational diagnostics and severity analysis techniques for COVID, such as multilevel threshold image segmentation for chest radiography 18 , deep learning methods for diagnosing COVID and its variant 19 , and analysis of COVID severity using evolutionary machine learning approaches by Shi Su et al. Moreover, Xiong et al. Data 2: The second data set is taken from paper of Jamal et al. It represents therelief times of 20 patients receiving analgesic. The data values are given as follows in the Table 5. Tables 6 and 7 revealed noteworthy observations: all information criteria associated with the NeS-BrIII model are consistently smaller when compared to the classical models. In stark contrast, the classical distributions exhibited unclear and ambiguous findings, primarily due to their inherent imprecision and errors. These limitations are notably absent in the NeS-BrIII distribution, making it a preferred choice for modeling and analysis. Naturally, we can observe that the projected model yields least results in comparison to traditional BrXII model which is the prerequisite for all these ICs based on a trade-off between model intricacy and goodness of fit. This study introduced a novel probabilistic model, the neutrosophic Burr-III distribution, tailored for applications in neutrosophic surface analysis. In the realm of real-world problem, our exploration of the neutrosophic Burr-III distribution has shown its aptitude in addressing data ambiguity and vagueness, an aspect where the classical Burr-III distribution falls short. The neutrosophic Burr-III distribution not only insights into reliability properties, moment expressions, order statistic, and entropy measures but also proves its versatility as a robust tool for deciphering complex data. To validate its practical significance, we applied the neutrosophic Burr-III distribution to real-world data sets, placing it in a head-to-head comparison with the well-known classical distributions. The outcomes of the analysis unequivocally demonstrated that the neutrosophic Burr-III distribution surpassed its classical counterpart in capturing the intricate nuances of the underlying data, signaling its potential as a superior modeling tool across various domains. Thus the neutrosophic Burr-III distribution opens up new avenues for addressing the complexities of real-world problems, where ambiguity is often the norm rather than the exception. This study also opens up several avenues for researchers and practitioners for future research in neutrosophic analysis and probabilistic modeling, ranging from the development of new models and algorithms paving the way for new insights, methodologies and applications in data analysis and decision making. However, this study acknowledges some limitations in specific contexts, such as theoretical and computational challenges. Moreover the study is valid only when the data is ambiguous and vague. If the data is crisp and well-defined the classical model is valid leaving no space for the neutrosophic analysis. However, we acknowledge limitations in specific contexts, such as theoretical and computational challenges. Gove, J. Foresty 81 2 , — Article Google Scholar. Wingo, D. MathSciNet Google Scholar. Maximum Likelihood Methods for fitting the Burr type XII distribution to multiply progressively censored life test data. Metrika 40 3—4 , — Chernobai, A. Google Scholar. Sherrick, B. Recovering probabilistic information from option markets: Tests of distributional assumptions. Future Markets 16 5 , — Mielke, P. Another family of distributions for describing and analyzing precipitation data. Tejeda, H. Modelling Crop Price through a Burr Distribution and analysis of correlation between crop prices and yields using copula method. Abdel-Ghaly, A. Dagum, C. New model of personal income distribution: Specification and estimation. Kleiber, C. Benjamin, S. Use of the dagum distribution for modeling tropospheric ozone levels. Alhasan, K. Alhabib, R. Some neutrosophic probability distributions. Neutrosophic Sets Syst. Patro, S. The neutrosophic statistical distribution, more problems, more solutions Infinite Study, Aslam, M. Neutrosophic Rayleigh distribution with some basic properties and application. Sherwani, R. Neutrosophic beta distribution with properties and applications. Almongy, H. Su, H. Multilevel threshold image segmentation for COVID chest radiography: A framework using horizontal and vertical multiverse optimization. Rafique, Q. Reviewing methods of deep learning for diagnosing COVID, its variants and synergistic medicine combinations. Shi, B. Analysis of COVID severity from the perspective of coagulation index using evolutionary machine learning with enhanced brain storm optimization. King Saud Univ. PubMed Google Scholar. Su, Y. Xiong, Y. Mobile Comput. Using moving averages to pave the neutrosophic time series. Neutrosophic Sci. A new sampling plan using neutrosophic process loss consideration. Symmetry Basel. Product acceptance determination with measurement error using the neutrosophic statistics. Fuzzy Syst. Attribute control chart using the repetitive sampling under neutrosophic system. IEEE Access 7 , — Burr, I. Cumulative frequency distributions. Gusmao, F. The generalized inverse Weibull distribution. Lindsay, S. Modeling the diameter distribution of forest stands using the Burr distribution. Smarandache, F. Neutrosophy: Neutrosophic probability, set, and logic: analytic synthesis and synthetic analysis Definitions derived from neutrosophics. Infinite Study Neutrosophy and neutrosophic logic. A unifying field in logics: neutrosophic logic. Neutrosophy, neutrosophic set, neutrosophic probability: Neutrosophic logic. Neutrosophy, neutrosophic set, neutrosophic probability Infinite Study, Salama, A. Neutrosophic crisp set theory Infinite Study, Neutrosophic crisp sets and neutrosophic crisp topological spaces Infinite Study, Introduction to neutrosophic statistics Introduction to neutrosophic measure, neutrosophic integral, and neutrosophic probability Shoukri, M. Sampling properties of estimators of the log-logistic distribution with application to Canadian precipitation data. Zeina, M. Neutrosophic random variables. Download references. The authors are deeply thankful to the editor and reviewers for their valuable suggestions to improve the quality and the presentation of the paper. You can also search for this author in PubMed Google Scholar. Correspondence to Muhammad Aslam. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. Reprints and permissions. Jamal, F. Sci Rep 14 , Download citation. Received : 07 February Accepted : 08 May Published : 11 May Anyone you share the following link with will be able to read this content:. Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative. Skip to main content Thank you for visiting nature. Download PDF. Abstract In this study, we have presented a novel probabilistic model called the neutrosophic Burr-III distribution, designed for applications in neutrosophic surface analysis. Birnbaum Saunders distribution for imprecise data: statistical properties, estimation methods, and real life applications Article Open access 23 March Estimating neutrosophic finite median employing robust measures of the auxiliary variable Article Open access 04 May Introduction Historically, in , Burr formulated twelve families of distributions through the Kearl Pearson equation, each offering distinct density functions with diverse applications. The model with properties In this section, we delve into the development of the neutrosophic model based on the classical Burr-III distribution. This method leverage neutrospohic statistics to estimate the parameters of the distribution from the observed data The model development If the random variable X follow the Burr-III distribution having CDF defined in Eq. Figure 1. Full size image. Figure 2. Figure 3. Full size table. Table 5 The data values for the data 1 and data 2. Table 6 MLEs and their standard errors in parentheses and goodness-of-fit statistics for models for data set 1. Table 7 MLEs and standard errors in parentheses and goodness-of-fit statistics for models for data set 2. Figure 4. Figure 5. Conclusion This study introduced a novel probabilistic model, the neutrosophic Burr-III distribution, tailored for applications in neutrosophic surface analysis. Data availability The data used in the article is given therein. References Gove, J. Article Google Scholar Wingo, D. Google Scholar Sherrick, B. Article Google Scholar Mielke, P. Article Google Scholar Dagum, C. Google Scholar Kleiber, C. Google Scholar Alhasan, K. Google Scholar Patro, S. Google Scholar Almongy, H. Google Scholar Su, H. Google Scholar Alhabib, R. Google Scholar Aslam, M. Article Google Scholar Burr, I. Article Google Scholar Gusmao, F. Article Google Scholar Smarandache, F. Google Scholar Smarandache, F. Google Scholar Download references. Acknowledgements The authors are deeply thankful to the editor and reviewers for their valuable suggestions to improve the quality and the presentation of the paper. View author publications. Ethics declarations Competing interests The authors declare no competing interests. Additional information Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. About this article. Cite this article Jamal, F. Copy to clipboard. Publish with us For authors Language editing services Submit manuscript. Search Search articles by subject, keyword or author. Show results from All journals This journal. Advanced search. Close banner Close. Email address Sign up. Get the most important science stories of the day, free in your inbox.

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