Another Family of Bivariate Distributions with Equivalent Independence and Uncorrelation

Considering the characteristics of the bivariate normal distribution, in which uncorrelation of two random variables is equivalent to their independence, it is interesting to verify this issue in other distributions; in other words; whether or not the multivariate normal distribution is the only distribution in which uncorrelation is equivalent to independence. This paper aims to answer this question by presenting some concepts and introduce another family in which uncorrelation is equivalent to independence.