Next-generation statistical methodology: Advances health science research

Accurately modeling health science data is crucial for advancing medical research and improving patient outcomes. Traditional statistical analysis methods face significant challenges due to the complexity and diversity of health sciences data. This article introduces a groundbreaking statistical framework designed to overcome these challenges by developing a next-generation family of distributions, with a special focus on the versatility of the Weibull distribution. The data used in this study has been thoroughly authenticated to ensure reliability and validity. Comprehensive Monte Carlo simulations revealed that the Maximum Product of Spacing Estimator is the most effective among seven-point estimation methods, according to standard metrics. Additionally, the study identifies optimal methods for analyzing various types of lifetime data, including the Maximum Product of Spacing Estimator for pharmaceutical efficacy (ED50), the Least Squares Estimator for psychiatric treatment durations, the Cramer-von Mises Estimator for data on 43 leukemia patients and for survival periods of 20 leukemia patients, and the Right Tail Anderson-Darling Estimator for remission times of 128 bladder cancer patients. The adaptability and flexibility of the next-generation Weibull distribution set it apart as the best match among its contemporaries

A new flexible distribution with applications to engineering data

In this work, we presented a new model called the alpha power inverse power Burr-Hatke distribution (APIPBHD). It provides several greater advantages in fitting a variety of different types of data. Estimates of the model parameters are provided and based on traditional research methods. We established the superiority of the proposed distribution by utilizing the importance and adaptability of the APIPBHD compared to other well-known distributions. The real data set includes 63 observations, all of which were manufactured to approximate the strengths of glass fibers to highlight the relevance and flexibility of the provided technique. We proved our superiority using one set of real data. Finally, major findings and conclusions are recorded at the end of the paper. Also, we added future work on the upcoming research depending on the proposed model

Photothermal effects induced by laser radiation in a 2D axi-symmetric generalized thermoelastic semiconducting half space using MGL model

In this paper, a novel model based on the strain-temperature rate-dependent theory is investigated to study the coupling influences of thermal, elastic, and plasma waves during the photothermal process in a 2D axi-symmetric semiconducting half space. The surface absorption technique is used to illuminate the surface of the medium by a laser beam whose temporal and spatial profiles are Gaussian, moreover, the surface is also considered traction free. Integral transform method is applied using Laplace and Hankel transformations to obtain a general solution to the considered problem. Inverse Laplace transform is obtained computationally using Rimann-Sum approximation. Silicon element is chosen as an application to show the compatibility of the results of the MGL model with GL and CTE models, moreover the relaxation times effects of the new model were studied

Statistical Inference for Competing Risks Model with Adaptive Progressively Type-II Censored Gompertz Life Data Using Industrial and Medical Applications

This study uses the adaptive Type-II progressively censored competing risks model to estimate the unknown parameters and the survival function of the Gompertz distribution. Where the lifetime for each failure is considered independent, and each follows a unique Gompertz distribution with different shape parameters. First, the Newton-Raphson method is used to derive the maximum likelihood estimators (MLEs), and the existence and uniqueness of the estimators are also demonstrated. We used the stochastic expectation maximization (SEM) method to construct MLEs for unknown parameters, which simplified and facilitated computation. Based on the asymptotic normality of the MLEs and SEM methods, we create the corresponding confidence intervals for unknown parameters, and the delta approach is utilized to obtain the interval estimation of the reliability function. Additionally, using two bootstrap techniques, the approximative interval estimators for all unknowns are created. Furthermore, we computed the Bayes estimates of unknown parameters as well as the survival function using the Markov chain Monte Carlo (MCMC) method in the presence of square error and LINEX loss functions. Finally, we look into two real data sets and create a simulation study to evaluate the efficacy of the established approaches

Statistical Inference for Competing Risks Model with Adaptive Progressively Type-II Censored Gompertz Life Data Using Industrial and Medical Applications

This study uses the adaptive Type-II progressively censored competing risks model to estimate the unknown parameters and the survival function of the Gompertz distribution. Where the lifetime for each failure is considered independent, and each follows a unique Gompertz distribution with different shape parameters. First, the Newton-Raphson method is used to derive the maximum likelihood estimators (MLEs), and the existence and uniqueness of the estimators are also demonstrated. We used the stochastic expectation maximization (SEM) method to construct MLEs for unknown parameters, which simplified and facilitated computation. Based on the asymptotic normality of the MLEs and SEM methods, we create the corresponding confidence intervals for unknown parameters, and the delta approach is utilized to obtain the interval estimation of the reliability function. Additionally, using two bootstrap techniques, the approximative interval estimators for all unknowns are created. Furthermore, we computed the Bayes estimates of unknown parameters as well as the survival function using the Markov chain Monte Carlo (MCMC) method in the presence of square error and LINEX loss functions. Finally, we look into two real data sets and create a simulation study to evaluate the efficacy of the established approaches

SARS-CoV-2 infection with lytic and non-lytic immune responses: A fractional order optimal control theoretical study

In this research article, we establish a fractional-order mathematical model to explore the infections of the coronavirus disease (COVID-19) caused by the novel SARS-CoV-2 virus. We introduce a set of fractional differential equations taking uninfected epithelial cells, infected epithelial cells, SARS-CoV-2 virus, and CTL response cell accounting for the lytic and non-lytic effects of immune responses. We also include the effect of a commonly used antiviral drug in COVID-19 treatment in an optimal control-theoretic approach. The stability of the equilibria of the fractional ordered system using qualitative theory. Numerical simulations are presented using an iterative scheme in Matlab in support of the analytical results

A Flexible Extension of Reduced Kies Distribution: Properties, Inference, and Applications in Biology

The extended reduced Kies distribution (ExRKD), which is an asymmetric flexible extension of the reduced Kies distribution, is the subject of this research. Some of its most basic mathematical properties are deduced from its formal definitions. We computed the ExRKD parameters using eight well-known methods. A full simulation analysis was done that allows the study of these estimators’ asymptotic behavior. The efficiency and applicability of the ExRKD are investigated via the modeling of COVID-19 and milk data sets, which demonstrates that the ExRKD delivers a better match to the data sets when compared to competing models

Weighted power Maxwell distribution: Statistical inference and COVID-19 applications.

During the course of this research, we came up with a brand new distribution that is superior; we then presented and analysed the mathematical properties of this distribution; finally, we assessed its fuzzy reliability function. Because the novel distribution provides a number of advantages, like the reality that its cumulative distribution function and probability density function both have a closed form, it is very useful in a wide range of disciplines that are related to data science. One of these fields is machine learning, which is a sub field of data science. We used both traditional methods and Bayesian methodologies in order to generate a large number of different estimates. A test setup might have been carried out to assess the effectiveness of both the classical and the Bayesian estimators. At last, three different sets of Covid-19 death analysis were done so that the effectiveness of the new model could be demonstrated

Bayesian Inferential Approaches and Bootstrap for the Reliability and Hazard Rate Functions under Progressive First-Failure Censoring for Coronavirus Data from Asymmetric Model

This paper deals with the estimation of the parameters for asymmetric distribution and some lifetime indices such as reliability and hazard rate functions based on progressive first-failure censoring. Maximum likelihood, bootstrap and Bayesian approaches of the distribution parameters and reliability characteristics are investigated. Furthermore, the approximate confidence intervals and highest posterior density credible intervals of the parameters are constructed based on the asymptotic distribution of the maximum likelihood estimators and Markov chain Monte Carlo technique, respectively. In addition, the delta method is implemented to obtain the variances of the reliability and hazard functions. Moreover, we apply two methods of bootstrap to construct the confidence intervals. The Bayes inference based on the squared error and LINEX loss functions is obtained. Extensive simulation studies are conducted to evaluate the behavior of the proposed methods. Finally, a real data set of the COVID-19 mortality rate is analyzed to illustrate the estimation methods developed here

Data analysis results for first real data.

Data analysis results for first real data.</p