Spherical CuS nanocrystals were synthesised via reflux (R) and hydrothermal (H) methods using copper acetate monohydrate (Cu (ac)₂·H₂O) and thioacetamide as precursors. This process was carried out in the absence and presence of cetyltrimethylammonium bromide (CTAB) and sodium dodecyl sulphate (SDS) surfactants. The products were characterised by using the methods of X-ray powder diffraction (XRD), scanning electron microscopy, energy-dispersive X-ray and transmission electron microscopy. According to XRD results, nanoparticles with the size of 16–23 nm were obtained. The effects of surfactant type, reaction time and reaction temperature on the morphology, yield, size and phase of the obtained products were investigated. According to this study, CTAB was more appropriate than SDS in obtaining uniform and spherical CuS nanoparticles.

In this paper, we consider the estimation of the probability density function and the cumulative distribution function of the inverse Rayleigh distribution. In this regard, the following estimators are considered: uniformly minimum variance unbiased estimator, maximum likelihood (ML) estimator, percentile estimator, least squares estimator and weighted least squares estimator. To do so, analytical expressions are derived for the mean integrated squared error. As the result of simulation studies and real data applications indicate, when the sample size is not very small the ML estimator performs better than the others.

This work considers a multifactor linear mixed model under heteroscedasticity in random-effect factors and the skew-normal errors for modeling the correlated datasets. We implement an expectation–maximization (EM) algorithm to achieve the maximum likelihood estimates using conditional distributions of the skew-normal distribution. The EM algorithm is also implemented to extend the local influence approach under three model perturbation schemes in this model. Furthermore, a Monte Carlo simulation is conducted to evaluate the efficiency of the estimators. Finally, a real data set is used to make an illustrative comparison among the following four scenarios: normal/skew-normal errors and heteroscedasticity/homoscedasticity in random-effect factors. The empirical studies show our methodology can improve the estimates when the model errors follow from a skew-normal distribution. In addition, the local influence analysis indicates that our model can decrease the effects of anomalous observations in comparison to normal ones.