Volume 20, Issue 4

Abstract. It was Azzalini (1985) who introduced the univariate skew normal distribution family with a shape parameter , and then extended skew normal distribution family by adding an additional shape parameters . Azzalini and Dalla Valle (1996) extended the results to the multivariate case. Basic properties for the univariate and multivariate cases were summarized by Azzalini (2005). Chen and Gupta (2005) considered the matrix variate skew normal distribution family and proposed the moment generating function and demonstrated that the distribution of the quadratic form of the skew normal matrix variate follows a Wishart distribution. Their results were generalized by Harrar and Gupta (2008). In this paper, we generalize the univariate extended skew normal distribution family to the matrix variate case. The moment generating function, the distribution of the quadratic form and the linear form, and the marginal and conditional distributions of this family are studied.

Abstract. We consider quantization of random continuous-valued signals. In practice, analogue signals are quantized at sampling points with further compression. We study probabilistic models for run-length encoding (RLE) algorithm applied to quantized sampled random signals (Gaussian processes). This compression technique is widely used in digital signal and image processing. The mean (inverse) RLE compression ratio (or data rate savings) and its statistical inference are considered. In particular, the asymptotic normality for some estimators of this characteristic is shown. Numerical experiments for synthetic and real data are presented.

Abstract. In this paper, we establish some strong convergence theorems of modified general composite implicit random iteration process to a common random fixed point for a finite family of asymptotically quasi-nonexpansive in the intermediate sense random operators.

Abstract. The Elliptic Law under the G -Lindeberg condition for the independent pairs of the entries of a random matrices having zero expectations, equal sums of their covariances and double stochastic matrix of variances of their array is proven.