Yazd University Journal of Statistical Modelling: Theory and Applications 2676-7392 6 2 2025 07 01 A generalized δ-shock model in the discrete-time framework 127 135 4223 10.22034/jsmta.2026.23871.1201 EN Reza Farhadian Department of Statistics‎, ‎Razi University‎, ‎Kermanshah‎, ‎Iran 0000-0003-4027-9838 Habib Jafari Department of Statistics‎, ‎Razi University‎, ‎Kermanshah‎, ‎Iran 0000-0001-5191-2796 Journal Article 2025 10 25 According to the δ-shock model‎, ‎a system subjected to random shocks fails when the inter-arrival time between two successive shocks is less than a critical threshold δ‎. ‎Several generalizations of the δ-shock model have been proposed to study shock-exposed systems in different scenarios‎. ‎In this paper‎, ‎we examine a recently proposed generalization of the δ-shock model within a discrete-time framework‎, ‎where inter-arrival times follow a geometric distribution‎. ‎We derive the probability generating function‎, ‎the mean time to failure‎, ‎and the variance of the system lifetime‎. ‎Furthermore‎, we present ‎an illustrative example related to crop insurance is presented to demonstrate the practical relevance and applicability of the proposed discrete-time model. https://jsm.yazd.ac.ir/article_4223_fe7f768018213b58d79d0cfd99e59f84.pdf