We define a new alternate measure of the cumulative residual Sharma-Taneja-Mittal entropy. For this measure, there are given upper and lower bounds, is introduced a consistent test based on the uniform distribution and some concrete numerical examples are formulated.

In this work, we consider the multivariate aggregate model introduced in [11], model that takes into account the case when different types of claims affect in the same time an insurance portfolio under some specific assumptions related to the number of claims. For the probability function of the corresponding multivariate compound distribution, [11] obtained an exact recursive formula proved using the properties of the probability generating function. In this paper, we present a new shorter proof of the same formula that we also extend to a new form. Moreover, we present an alternative approximate method to evaluate the compound distribution based on the Fourier transform, and we compare both methods on a numerical example.

In the contemporary digital landscape, AI (Artificial Intelligence) emerged as a pivotal tool in enhancing the defense technologies developed across the entire network infrastructure. As reliance on AI-based decision-making grew, so did the imperative need for interpretability, transparency, and trustworthiness, leading to the development and integration of XAI (eXplainable Artificial Intelligence). This research paper provides a comprehensive overview of the current state of the art in XAI approaches that can be effectively implemented for network traffic monitoring, especially in critical digital infrastructures. The main contribution of this research article consists of the comparative analysis of the XAI SHAP (Shapley Additive Explanation) method applied to different datasets obtained from real-time network traffic monitoring, utilizing several representative parameters, which demonstrates the performance, vulnerabilities, and limitations of the proposed method, and also the security implications of the system resources from a cybersecurity perspective. Experimental results show that Ethernet networks offer higher predictability and clearer decision boundaries. Consequently, they are a safer solution for deployment in sensitive network architectures. In contrast, BYOD (Bring Your Own Device) Wi-Fi environments exhibit greater randomness.