On characterizations of some bivariate continuous distributions by properties of higher-degree bivariate stop-loss transforms

In this paper we study some characteristic properties of higher-degree bivariate stop-loss transforms (partial moments). A new bivariate distribution is proposed by extending the characterizing identity of univariate partial moments due to Lin (2003 Lin, G. D. 2003. Characterizations of the exponential distribution via the residual lifetime. Sankhyā: The Indian Journal of Statistics, Series A 65 (2):249–58. [Google Scholar]) to the bivariate case. A real-data analysis is also carried out to illustrate the theoretical results.