Ali Dolati - Department of Statistics, , Ferdowsi University of Mashhad, Mashhad, Iran
Mohammad Amini - Department of Statistics, , Ferdowsi University of Mashhad, Mashhad, Iran
G. R. Mohtashami Borzadaran - Department of Statistics, , Ferdowsi University of Mashhad, Mashhad, Iran

‎In probability and statistics‎‎ the earliest concept related to independence is the uncorrelatedness. ‎It is well known that a pair of independent random variables are uncorrelated‎, ‎but uncorrelated random variables may or may not be independent‎.‎The aim of this paper is to provide some new models for the joint distribution of the uncorrelated random variables that are not independent. ‎The proposed models include a bivariate mixture structure, a transformation method, and copula method. Several examples illustrating the results are included.

‎Copula‎, ‎Dependent‎, ‎Independent‎, Sub-independence, ‎Uncorrelated‎‎‎