For a class of skew-normal matrix distributions, the density function, moment generating function and independent conditions are obtained. The noncentral skew Wishart distribution is defined and the necessary and sufficient conditions under which a quadratic form is noncentral skew Wishart distributed random matrix are established. A new version of Cochran’s theorem is given. For illustration, ...

This paper presents a study of skew — highly variable task runtimes — in MapReduce applications. We describe various causes and manifestations of skew as observed in real world Hadoop applications. Runtime task distributions from these applications demonstrate the presence and negative impact of skew on performance behavior. We discuss best practices recommended for avoiding such behavior and t...

According to a well-known theorem of Cramér and Wold, if P Q are two Borel probability measures on Rd whose projections PL,QL onto each line L in satisfy PL=QL, then P=Q. Our main result is that, both elliptical distributions, then, show that P=Q, it suffices merely check PL=QL for certain set (d2+d)/2 lines L. Moreover optimal. The class distributions contains the Gaussian as well many other m...