A class of flexible weighted distributions for modelling and analyzing non-normal data

This paper introduces a class of weighted normal distributions, which includes the normal and skew-normal distributions as its special members. This class is defined as the marginal distribution of a bivariate normal-doubly truncated noncentral t distribution and studied from several aspects such as weighting of normal density functions, inequality constrained distributions, scale mixture of bivariate normal and probabilistic representations. The relationships among these aspects are given, and various properties of the class are also discussed. Necessary theories and two applications are provided.