New Families of Distributions for Modeling Bivariate Data, with Applications

Abstract

In this study we introduce a new method of adding two shape parameters to any baseline bivariate distribution function (df) to get a more flexible family of bivariate df's. Through the additional parameters we can fully control the type of the resulting family. This method is applied to yield a new two-parameter extension of the bivariate standard normal distribution, denoted by BSSN. The statistical properties of the BSSN family are studied. Moreover, via a mixture of the BSSN family and the standard bivariate logistic df, we get a more capable family, denoted by FBSSN. Theoretically, each of the marginals of the FBSSN contains all the possible types of df's with respect to the signs of skewness and excess kurtosis. In addition, each possesses very wide range of the indices of skewness and kurtosis. Finally, we compare the families BSSN and FBSSN with some important competitors (i.e., some generalized families of bivariate df's) via real data examples. AMS 2010 Subject Classification: 62-07; 62E10; 62F99.