In this paper we consider several generalizations of the skew t-normal distribution, and some of their properties. Also, we represent several theorems for constructing each generalized skew t-normal distribution. Next, we illustrate the application of the proposed distribution studying the ratio of two heavy metals, Nickel and Vanadium, associated with crude oil in Shadgan wetland in the south-...

This paper studies a single-stage production system, two-stage production system where specification limits are designed for inspection. When quality characteristics fall below a lower threshold or above an upper threshold, a decision is made to rework or scrap the item. The target is to determine the optimum target for a process based on rework or scrap costs. In contrast to previous studies, ...

The characteristic function of the folded normal distribution and its moment function are derived. The entropy of the folded normal distribution and the Kullback–Leibler from the normal and half normal distributions are approximated using Taylor series. The accuracy of the results are also assessed using different criteria. The maximum likelihood estimates and confidence intervals for the param...

It is well-known that the skew-normal distribution can provide an alternative model to the normal distribution for analyzing asymmetric data. The aim of this paper is to propose two goodness-of-fit tests for assessing whether a sample comes from a multivariate skew-normal (MSN) distribution. We address the problem of multivariate skew-normality goodness-of-fit based on the empirical Laplace tra...

The multivariate normal density is a monotonic function of the distance to the mean, and its ellipsoidal shape is due to the underlying Euclidean metric. We suggest to replace this metric with a locally adaptive, smoothly changing (Riemannian) metric that favors regions of high local density. The resulting locally adaptive normal distribution (LAND) is a generalization of the normal distributio...

Introduction: 18F-Choline PET-CT is an increasingly used technique in patients with prostate cancer. The main indication is to localise the disease in patients with biochemical recurrence. To accurately interpret 18F-Choline PET, knowledge of normal tracer distribution is paramount. The aim of this study was to describe the normal distribution pattern of 18F-Cho...

In this paper, the matrix variate ^-generalized normal distribution is introduced. Then its properties are studied. In particular, it is proved that this distribution has maximal entropy in a certain class of distributions.

The Ellipsoid NDF is a new normal distribution function (NDF) that we introduce and use in the accompanying paper. It can be used with micro-facet BRDF to model the reflection and refraction of light from surfaces. This new distribution is a generalization of the widely used isotropic GGX/Trowbridge-Reitz distribution. The Ellipsoid model is based on the surface statistics of an arbitrary 3D el...