Analysis of Dependent Variables Following Bivariate J-shaped Distribution and Methods to Construct New Bivariate Classes

Abstract

A J-shaped distribution called inverted Topp-Leone (ITL) is discussed in this paper in both one and two dimensions. The bivariate inverted Topp-Leone (BITL) distribution is introduced as a shock Model. The mathematical properties of ITL   and  BITL  distributions are discussed. All the characteristic functions for both ITL   and  BITL  distributions are obtained explicitly in compact forms. For the unknown parameters, maximum likelihood estimation is applied and the exact information matrix is derived. Two new methods for constructing bivariate distributions from BITL distribution are discussed in detail.

Consequently, generalized and exponentiated ITL distributions are defined in both univariate and bivariate cases. An absolutely continuous BITL distribution and its properties are also discussed. A real data set is then re-analyzed for illustration.