A class of continuous bivariate distributions with linear sum of hazard gradient components

*Correspondence: [email protected] Department of Statistics, University of São Paulo, São Paulo, Brazil Abstract The main purpose of this article is to characterize a class of bivariate continuous non-negative distributions such that the sum of the components of underlying hazard gradient vector is a linear function of its arguments. It happens that this class is a stronger version of the Sibuya-type bivariate lack of memory property. Such a class is allowed to have only certain marginal distributions and the corresponding restrictions are given in terms of marginal densities and hazard rates. We illustrate the methodology developed by examples, obtaining two extended versions of the bivariate Gumbel’s law.