Following the methodology developed by (Comput. Math. Appl. 33 (1997) 81–104), we define a discrete version of gradient vector and associated line integral along arbitrary path connecting two nodes of uniform grid. An exponential representation of joint survival function of bivariate discrete non-negative integer-valued random variables in terms of discrete line integral is established. We apply it to generate a discrete analogue of the Sibuya-type aging property, incorporating many classical and new bivariate discrete models. Several characterizations and closure properties of this class of bivariate discrete distributions are presented.
"Discrete line integral on uniform grids: Probabilistic interpretation and applications." Braz. J. Probab. Stat. 34 (4) 821 - 843, October 2020. https://doi.org/10.1214/19-BJPS454