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In this article, the stochastic fractional Davey-Stewartson equations (SFDSEs) that result from multiplicative Brownian motion in the Stratonovich sense are discussed. We use two different approaches, namely the Riccati-Bernoulli sub-ordinary differential equations and sine-cosine methods, to obtain novel elliptic, hyperbolic, trigonometric, and rational stochastic solutions. Due to the significance of the Davey-Stewartson equations in the theory of turbulence for plasma waves, the discovered solutions are useful in explaining a number of fascinating physical phenomena. Moreover, we illustrate how the fractional derivative and Brownian motion affect the exact solutions of the SFDSEs using MATLAB tools to plot our solutions and display a number of three-dimensional graphs. We demonstrate how the multiplicative Brownian motion stabilizes the SFDSE solutions at around zero.

In this article, we take into account the stochastic Kuramoto-Sivashinsky equation forced by multiplicative noise in the Itô sense. To obtain the exact stochastic solutions of the stochastic Kuramoto-Sivashinsky equation, we apply the G′G\frac{{G}^{^{\prime} }}{G}-expansion method. Furthermore, we extend some previous results where this equation has not been previously studied in the presence of multiplicative noise. Also, we show the influence of multiplicative noise on the analytical solutions of the stochastic Kuramoto-Sivashinsky equation.

The fundamental objective of this article is to find exact solutions to the stochastic fractional-space Allen–Cahn equation, which is derived in the Itô sense by multiplicative noise. The exact solutions to this equation are required since it appears in many discipline areas including plasma physics, quantum mechanics and mathematical biology. The tanh–coth method is used to generate new hyperbolic and trigonometric stochastic and fractional solutions. The originality of this study is that the results produced here expand and improve on previously obtained results. Furthermore, we use Matlab package to display 3D surfaces of analytical solutions derived in this study to demonstrate the effect of stochastic term on the solutions of the stochastic-fractional-space Allen–Cahn equation.

The intertwining relationship between sustainability and discrete probability distributions found its significance in decision-making processes and risk assessment frameworks. Count data modeling and its practical applications have gained attention in numerous research studies. This investigation focused on a particular discrete distribution characterized by a single parameter obtained through the survival discretization method. Statistical attributes of this distribution were accurately explicated using generalized hypergeometric functions. The unveiled characteristics highlighted its suitability for analyzing data displaying "right-skewed" asymmetry and possessing extended "heavy" tails. Its failure rate function effectively addressed scenarios marked by a consistent decrease in rates. Furthermore, it proved to be a valuable tool for probabilistic modeling of over-dispersed data. The study introduced various estimation methods such as maximum product of spacings, Anderson-Darling, right-tail Anderson-Darling, maximum likelihood, least-squares, weighted least-squares, percentile, and Cramer-Von-Mises, offering comprehensive explanations. A ranking simulation study was conducted to evaluate the performance of these estimators, employing ranking techniques to identify the most effective estimator across different sample sizes. Finally, real-world sustainability engineering and medical datasets were analyzed to demonstrate the significance and application of the newly introduced model. [ABSTRACT FROM AUTHOR]

In this article, we introduce some reliability concepts for the bivariate Pareto Type II distribution including joint hazard rate function, CDF for parallel and series systems, joint mean residual lifetime, and joint vitality function. The maximum likelihood and Bayesian estimation methods are utilized to estimate the model parameters. Simulation is carried out to assess the performance of the maximum likelihood and Bayesian estimators, and it is found that the two approaches work quite well in estimation process. Finally, a real lifetime data is analyzed to show the flexibility and the importance of the introduced bivariate mode. [ABSTRACT FROM AUTHOR]

In this study, we introduce a novel estimation technique for assessing the reliability parameter R = P (Y < X) of the uniform truncated negative binomial distribution (UTNBD) in the context of stress–strength analysis. We base our inferences on the assumption that both the strength (X) and stress (Y) random variables follow a UTNBD with identical first shape and scale parameters. In the presence of a progressive type-II censoring scheme, we employ maximum likelihood, two parametric bootstrap methods, and Bayesian estimation approaches to derive the estimators. Due to the complexity introduced by censoring, the estimators are not available in explicit forms and are instead obtained through numerical approximation techniques. Furthermore, we compute the highest posterior density credible intervals and determine the asymptotic variance-covariance matrix. To assess the performance of our proposed estimators, we conduct a Monte Carlo simulation study and provide a comparative analysis. Finally, we illustrate the practical applicability of our study with an engineering application. [ABSTRACT FROM AUTHOR]

In this paper, we define a new generator to propose continuous as well as discrete families (or classes) of distributions. This generator is used for the DAL model (acronym of the last names of the authors, Dimitrakopoulou, Adamidis, and Loukas). This newly proposed family may be called the new odd DAL (NODAL) G-class or alternate odd DAL G-class of distributions. We developed both a continuous as well as discrete version of this new odd DAL G-class. Some mathematical and statistical properties of these new G-classes are listed. The estimation of the parameters is discussed. Some structural properties of two special models of these classes are described. The introduced generators can be effectively applied to discuss and analyze the different forms of failure rates including decreasing, increasing, bathtub, and J-shaped, among others. Moreover, the two generators can be used to discuss asymmetric and symmetric data under different forms of kurtosis. A Monte Carlo simulation study is reported to assess the performance of the maximum likelihood estimators of these new models. Some real-life data sets (air conditioning, flood discharges, kidney cysts) are analyzed to show that these newly proposed models perform better as compared to well-established competitive models. [ABSTRACT FROM AUTHOR]

The majority of approaches proposed in the past few decades to solve life test problems have differed markedly from those used for closely related, yet broader, issues. Due to the complexity of data that are generated each day in many practical domains, as a result of the development of scales for rating the success or failure of reliability, a new domain of reliability has been created. This domain is referred to as life classes, where specific probability distributions are presented. In this study, it is shown that the use of the quality-of-fit technique to solve problems involving life testing makes sense, and produces simpler processes that are roughly equivalent or superior to those used in traditional procedures. They may also behave better in limited samples. This work investigates a novel quality-of-fit test statistic; it is based on an exponential transform and is compared to the best renewal used Laplace test in increasing convex ordering (NBRULC). Evidence for approach normality is provided. The calculated variables include powers, Pitman asymptotic effectiveness, and critical points. Methods on how to handle censored data were also studied. Our experiments have real-world applications in the fields of medicine and engineering. [ABSTRACT FROM AUTHOR]

A novel four-parameter lifetime Lomax model is presented and investigated within the scope of this paper. The failure rate of the innovative model can be "monotonically decreasing failure rate," "monotonically increasing failure rate," or "constant failure rate," and the density of the model can be "asymmetric right skewed," "symmetric," "asymmetric left skewed," or "uniform density". The new density is expressed as a blend of the Lomax densities that have been multiplied by an exponent. New bivariate Lomax types were created for our research. The maximum likelihood technique was utilized. We performed simulated experiments for the purpose of evaluating the finite sample behavior of maximum likelihood estimators, using "biases" and "mean squared errors" as our primary metrics of analysis. The novel distribution was evaluated based on a number of pertinent Lomax models, including Lomax extensions that were generated on the basis of odd log-logistic, Kumaraswamy, beta, gamma, and Topp–Leone families, among others. The newly developed extension demonstrated its relevance by predicting the service and failure times of datasets pertaining to aircraft windshields. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Due to the complexity of the data being generated day in and day out in many practical domains, as a result of the development of scales for rating the success or failure of reliability, a new domain of reliability called the classes of life and determinant probability distributions has been presented. This article introduces novel statistical probability models for the reliability class of life test under different reliability processes in the age range t ∘ . Several probabilistic properties and features were derived and rigorously screened to test the new reliability class. According to the U-statistic, a novel hypothesis test was created to evaluate the exponentiality property. The comparative efficiency of the test according to Pitman's asymptotic efficiency was examined and compared with other reliability classes. To prove the superiority of the new reliability class, some probability models were utilized, including the Weibull, Makeham, gamma, and linear failure rate models. Moreover, critical point simulations of the null Monte Carlo distribution and some applications of the censored and uncensored data were implemented to validate the class test listed by the reliability analysis. [ABSTRACT FROM AUTHOR]