Sameh Askar

There are numerous studies where data on population units’ auxiliary variables and attributes are simultaneously available. Therefore, due to cost-effectiveness and ease of recording, the study variable and several linearly related auxiliary variables are recorded. These auxiliary variables are commonly observed as quantitative and qualitative (attributes) variables and are jointly used to estimate the study variable’s population mean using a mixture estimator. In order to achieve this, a family of generalized mixture estimators was proposed under simple random sampling with the aim of improving performance under symmetrical and asymmetrical distributions. In addition, the estimator’s behavior for various sample sizes was examined with regard to its convergence to the normal distribution. The suggested generalized mixture estimator’s mean square error is deduced up to the first order of approximation. It is discovered that for the normal, uniform, Weibull, and gamma distributions, the suggested estimator estimates the population mean of the study variable with greater accuracy than the competing estimators. It is also revealed that when the proposed estimator converges to normality, the sample size is at least taken as 110, 1000, and 120. Furthermore, the implementation of three real-life datasets related to the finance and health sectors is also presented to support the proposed estimator’s significance.

The term “optical thermoelasticity” is used to describe how the optical properties of a material change when it is heated or deformed mechanically. The issues of effective elastic and heat transfer symmetry are given particular focus. This study gives a new nonlocal theoretical formulation for a thermo-optical elastic material that can be used to describe how thermomechanical waves and plasma waves relate to the symmetry of semiconductor materials such as silicon or germanium. The suggested model includes the idea of nonlocal elasticity and a modified Moore–Gibson–Thompson (MGT) heat conduction equation with nonsingular fractional derivative operators. The heat transfer equation has been converted and generalized into a nonsingular fractional form based on the concepts of Atangana and Baleanu (AB) using the Mittag–Leffler kernel. The developed model is used to examine the effect of thermal loading by ramp-type heating on a free plane of unbounded semiconductor material symmetries. Using the Laplace transform approach, we may analytically obtain linear solutions for the investigated thermo-photo-elastic fields, such as temperature. The Discussion section includes a set of graphs that were generated using Mathematica to evaluate the impact of the essential parameters.