By equal mean, two skew-symmetric families with the same kernel are quite similar, and the tails are often very close together. We use this observation to approximate the tail distribution of the skew-normal by the skew-normal-Laplace, and accordingly obtain a normal function approximation to...

A severe limitation of the original autoregressive process of order one or AR(1) process is the Gaussian nature of the assumed residual error distribution while the observed sample residual errors tend to be much more skewed and have a much higher kurtosis than is allowed by a normal...

The exact probability distribution of the first digit of integer powers up to an arbitrary but fixed number of digits is derived. Based on its asymptotic distribution, it is shown that it approaches Benford's law very closely for sufficiently high powers

Based on the method of copulas, we construct a parametric family of multivariate distributions using mixtures of independent conditional distributions. The new family of multivariate copulas is a convex combination of products of independent and comonotone subcopulas. It fulfills the four most...