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.

Thermal efficiency in conventional nanoliquids and hybrid nanofluid is one of the potential areas of research nowadays and multifariously applicable in broad industrial and engineering zone. The hybrid nanofluids have their own importance due to their enhanced thermal conductivity and better conductor for heat transfer. Therefore, the comparative study is performed conventional, and hybrid nanofluids are synthesized by Cu and Al₂O₃ with water as a base solvent. The novel nonlinear thermal radiations effects are introduced in the constitutive model and then furnished the results for the flow regimes (velocity, thermal behavior, shear stresses and local Nusselt number) by varying the physical constraints. Further, it is executed that the hybrid nanoliquids have ultra-high thermal performance than simple nanoliquid due to the addition of Al₂O₃. Finally, validation of the study is performed by restricting our model to some physical constraints and found them in excellent agreement with previously published work.

In this article, a new flexible probability density function with three parameters is proposed for modeling asymmetric data (positive and negative) with different types of kurtosis (mesokurtic, leptokurtic and platykurtic). Some of its statistical and reliability properties, including hazard rate function, moments, moment generating function, incomplete moments, mean deviations, moment of the residual life, moment of the reversed residual life, and order statistics are derived. Its hazard rate function can be either constant, increasing-constant, decreasing-constant, U shape, upside down shape or upside down-U shape. Seven classical estimation methods are considered to estimate the unknown model parameters. Monte Carlo simulation experiments are performed to compare the performance of the seven different estimation methods. Finally, a distinctive asymmetric real data application is analyzed for illustrating the flexibility of the new model.

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.

Outlying observations have a large influence on the linear model selection process. In this article, we present a novel approach to robust model selection in linear regression to accommodate the situations where outliers are present in the data. The model selection criterion is based on two components, the robust conditional expected prediction loss, and a robust goodness-of-fit with a penalty term. We estimate the conditional expected prediction loss by using the out-of-bag stratified bootstrap approach. In the presence of outliers, the stratified bootstrap ensures that we obtain bootstrap samples that are similar to the original sample data. Furthermore, to control the undue effect of outliers, we use the robust MM-estimator and a bounded loss function in the proposed criterion. Specifically, we observe that instead of minimizing the penalized loss function or the conditional expected prediction loss separately, it is better to minimize them simultaneously. The simulation and real-data based studies confirm the consistent and satisfactory behavior of our bootstrap model selection procedure in the presence of response outliers and covariate outliers.

Introduction: This paper aims to measure the performance of early detection methods, which are usually used for infectious diseases. Methodology: By using real data of confirmed Coronavirus cases from the Kingdom of Saudi Arabia and Italy, the moving epidemic method (MEM) and the moving average cumulative sums (Mov. Avg Cusum) methods are used in our simulation study. Results: Our results suggested that the CUSUM method outperforms the MEM in detecting the start of the Coronavirus outbreak.