A Bivariate Mixture of Chi-Normal Distribution and Bounded Students’ t-Distribution

Abstract

A bivariate mixture of Chi and Normal distribution is introduced by using Jacobian transformation and rescaling the scale, shape parameters of existing Mckay’s Bivariate Gamma distribution which is considered to be the chi-normal distribution and its marginals are univariate chi and normal distribution respectively. Conditional distribution, various generating functions and its constants are shown. Similarly, the authors explored a new Bounded student’s t-distribution in the sampling literature based on chi-normal mixture and studied its characteristics, computed the percentage points at 5% and 1% level by using Maple version 16. Three-dimensional probability surfaces are visualized the shape of chi-normal densities and two-dimensional probability curves shown the shape of Bounded student’s t density heuristically. Finally, the authors confirmed the limiting distribution of bounded student’s t distribution is the standard normal and the application of Bounded student’s t distribution was also numerically illustrated.