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This research presents a model called the 'Gaussian negative binomial mixture with a latent class choice model', which serves as a robust and efficient tool for analyzing decisions across different areas. Our innovative model combines elements of mixture models, negative binomial distributions, and latent class choice modeling to create an approach that captures the complexities of decision-making processes. We explain how the model is formulated and estimated, showcasing its effectiveness in analyzing and predicting choices in scenarios. Through the use of a dataset, we demonstrate the performance of this method, marking a significant advancement in choice modeling. Our results highlight the applications of this model and point towards promising directions for future research, especially in exploring symmetrical patterns and structures, within decision-making processes. [ABSTRACT FROM AUTHOR]

This study explores the concept of residual entropy as an alternative approach to traditional entropy measures. The field of information theory, built upon Shannon's entropy, has been instrumental in understanding the dynamics of systems. However, existing literature has recognized the limitations of applying traditional entropy measures to systems that have already been in existence for a certain duration. This study delves into the concept of residual entropy, acknowledging the need for a more suitable approach for such systems. Specifically, we investigate the characteristics of residual entropy using a quantile-based framework. By deriving the quantile residual entropy function for various lifetime models, we gain insights into the reordering and ageing phenomena captured by the quantile version of the residual entropy equation. Our findings contribute to an enhanced understanding of residual entropy and provide a novel perspective on analyzing and interpreting the behavior of established systems. [ABSTRACT FROM AUTHOR]

The development of certain aspects of hybrid special polynomials after incorporating monomiality principle, operational rules, and other properties and their aspects is obvious and indisputable. The study presented in this paper follows this line of research. By using the monomiality principle, new outcomes are produced, thus in line with prior facts, our aim is to introduce the degenerate 2D bivariate Appell polynomials Rmj (u, v; h). Further, we obtain some wellknown main properties and explicit forms satisfied by these polynomials. Also, generating relations corresponding to the degenerate 2D bivariate Bernoulli, Euler, and Genocchi polynomials are established, they will further be helpful in establishing the corresponding results for these polynomials. [ABSTRACT FROM AUTHOR]

Many researchers measure the uncertainty of a random variable using quantile-based entropy techniques. These techniques are useful in engineering applications and have some exceptional characteristics than their distribution function method. Considering order statistics, the key focus of this article is to propose new quantile-based Mathai-Haubold entropy and investigate its characteristics. The divergence measure of the Mathai-Haubold is also considered and some of its properties are established. Further, based on order statistics, we propose the residual entropy of the quantile-based Mathai-Haubold and some of its property results are proved. The performance of the proposed quantile-based Mathai-Haubold entropy is investigated by simulation studies. Finally, a real data application is used to compare our proposed quantile-based entropy to the existing quantile entropies. The results reveal the outperformance of our proposed entropy to the other entropies. [ABSTRACT FROM AUTHOR]

Introduction: The concentration of fluid and its analysis in human skin is innately a challenge due to its continuous movement and involvement in maximum life processes. The concentration of the fluid gets affected by the diffusion of fluids through the skin, which acts as the main barrier between the human body and the external environment. Therefore, it becomes imperative to study the process and impact of the diffusion of fluids through the skin. The problem becomes more interesting when the human body is immersed in water., Objectives: The present paper studies the change in the fluid distribution of human skin during its immersion in water of different temperatures. The application part of the paper visualizes various impaired vascular function and muscle soreness by water immersion during the physiotherapy treatment., Methods: A mathematical model based on the two-dimensional diffusion equation, along with appropriate boundary conditions, has been formulated. The maximum of the relevant parameters, such as fluid regulation, transfer coefficient, evaporation rate, etc., influencing the fluid distribution, have been incorporated. The model has been solved by variational finite element method, and numerical results have been obtained by the Crank-Nicholson scheme., Results: The increase in fluid concentration due to treatment with cold and acute hot water immersion has been noted, and the role of water immersion in enhancing the recovery in exercise-induced muscular damage has been analyzed., Conclusions: The paper addressed the issue of rate of water diffusion through human skin, which otherwise couldn't be drawn from the analogy of gas diffusion through the membrane due to the variation in permeabilities of the two processes. The paper has applications in water immersion therapies and other activities like monitoring swimming induced pulmonary edema, etc., (© 2020 The Authors. Published by Elsevier B.V. on behalf of Cairo University.)