The parametric Welch t-test and the non-parametric Wilcoxon–Mann–Whitney, empirical and exponential empirical likelihood tests are commonly used for hypothesis testing of two population means. In order to circumvent the inflated type I error problem of the non-parametric likelihood testing procedures, a simple calibration using the t distribution and bootstrapping is proposed. Those testing procedures are then being compared via extensive Monte Carlo simulations on the grounds of type I error and power. Evidence is provided supporting that (a) the t calibration and bootstrap improve the type I error of the non-parametric likelihoods, (b) the Welch t-test attains the type I error and produces high levels of power, and (c) the Wilcoxon–Mann–Whitney test produces inflated type I error while computation of the exact p-value is not feasible in the presence of ties. An application to real gene expression data illustrates the computational superiority of the Welch t-test.

Compositional data are positive multivariate data with unity sum constraint that have emerged over the last years in numerous scientific fields. Ever since, numerous models and approaches have been proposed for analyzing such data in the last 40 years. We list some of their properties and difficulties and review many techniques proposed over this period. In particular, we focus on transformations, distributions, regression models, discriminant analysis and clustering techniques, dimensionality reduction techniques, variable selection algorithms and finally we list some books and R packages developed for compositional data analysis.

A unique methodology due to the effect of stochastic heating is utilized to study the Moisture Diffusivity influence of an elastic semiconductor medium under the effect of photo-thermoelasticity theory. Accurately, random processes are applied at the boundary of the semiconductor medium. The governing equations are expressed in the one-dimensional form (1D). The boundary conditions are considered random; the additional noise is regarded as white noise. The problem is set up to investigate the interaction between moisture diffusivity, thermo-elastic waves, and plasma waves. The investigation is carried out during a photothermal transport procedure while taking moisture diffusivity into consideration. The Laplace transform is used to solve the problem. The numerical solution for field distribution is obtained using the short-time approximation while performing inverse transformations of Laplace. The Wiener process notion has been used to arrive at the solutions for the stochastic case. Silicon (Si) material is used along several sample paths in a numerical study based on stochastic simulation. Additionally, a comparison of the stochastic and deterministic field variable distributions is provided. The effects of thermoelectric, thermoelastic, and reference moisture parameters of the applied force on all physical distributions are discussed graphically.

Compositional data arise in many real-life applications and versatile methods for properly analyzing this type of data in the regression context are needed. When parametric assumptions do not hold or are difficult to verify, non-parametric regression models can provide a convenient alternative method for prediction. To this end, we consider an extension to the classicalk- Nearest Neighbours (k-NN) regression, that yields a highly flexible non-parametric regression model for compositional data. A similar extension of kernel regression is proposed by adopting the Nadaraya–Watson estimator. Both extensions involve a power transformation termed the $$\alpha $$α -transformation. Unlike many of the recommended regression models for compositional data, zeros values (which commonly occur in practice) are not problematic and they can be incorporated into the proposed models without modification. Extensive simulation studies and real-life data analyses highlight the advantage of using these non-parametric regressions for complex relationships between compositional response data and Euclidean predictor variables. Both the extendedK-NNand kernel regressions can lead to more accurate predictions compared to current regression models which assume a, sometimes restrictive, parametric relationship with the predictor variables. In addition, the extendedk-NNregression, in contrast to current regression techniques, enjoys a high computational efficiency rendering it highly attractive for use with large sample data sets.