At high angular frequencies, beyond the damping tail of the primary cosmic microwave background (CMB) power spectrum, the thermal Sunyaev–Zel’dovich (tSZ) effect constitutes the dominant signal in the CMB sky. The tSZ effect is caused by large-scale pressure fluctuations in the baryonic distribution in the universe, such that its statistical properties provide estimates of corresponding propert...

In this paper, a class of multivariate skew distributions has been explored. Then its properties are derived. The relationship between the multivariate skew normal and the Wishart distribution is also studied. @ 2003 Elsevier Science Ltd. All rights reserved. Keywords-Skew normal distribution, Wishart distribution, Moment generating function, Moments. Skewness.

Web Appendix A. Multivariate Skew Distributions Different versions of the multivariate skew–normal(SN) and skew-t (ST) distributions have been considered and used in the literature (Arellano-Valle and Genton, 2005; Arellano-Valle et al, 2007; Azzalini and Capitanio, 2003; Sahu et al, 2003 and among others). A new class of distributions by introducing skewness in multivariate elliptically distri...

In nonlinear time series analysis, the mixture autoregressive model (MAR) is an effective statistical tool to capture multimodality of data. However, traditional methods usually need assume that error follows a specific distribution not adaptive dataset. This paper proposes via asymmetric exponential power distribution, which includes normal skew-normal generalized Laplace and uniform as specia...