In this paper, we propose an alternative generalization of a recent test for univariate normality which is based on the empirical moment Generating Function to the multivariate case. We show, among other properties, that the proposed weighted L2-class of statistics is affine invariant and consistent. The empirical critical values of the proposed test are evaluated for different sample sizes, variable dimensions and values of the smoothing parameter through large scale simulations. The empirical power comparison of the test with a strong competitor shows that the test has a considerably high power performance, especially at large sample sizes as well as under heavy-tailed alternative distributions. The application of the statistic, together with its competitor, to six real-life datasets also supports the considerable good power performance of the proposed statistic as well as its ease of application.

In this note we propose an extended skew-Laplace distribution. We obtain explicit expressions for moment Generating Function and the two first moments of this distribution. Next, we show that the distribution of a linear combination of order statistics from a bivariate Laplace distribution can be expressed as a mixture of extended skew-Laplace distributions. This mixture representation enables us to derive moment Generating Function and moments of this linear combination.

In this study, a generalization of the Pell sequence called bi-periodic Pell sequence is carried out to matrix theory. Therefore, we call this matrix sequence the bi-periodic Pell matrix sequence whose entries are bi-periodic Pell numbers. Then the Generating Function, Binet formula and some basic properties and sum formulas are examined.

In this paper, a new generalization of the half-normal distribution which is called the perturbed half-normal distribution is introduced. The new distribution belongs to a family of distributions which includes the half-normal distribution along with an extra parameter to regulate skewness. The probability density Function (pdf) is derived and some various properties of the new distribution are obtained. The derived properties include the cumulative distribution Function (cdf), the rth moment, moment Generating Function, characteristic Function, mean deviation about the mean and estimation of the parameters using the method of moments and maximum likelihood. Finally, the flexibility and potentiality of the new distribution is illustrated in an application to two real data sets.