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Data breaches cause millions of dollars in financial losses each year. The insurance industry has been exploring the ways to transfer such extreme risk. In this work, we investigate data breach cat...

Malicious hacking data breaches cause millions of dollars in financial losses each year, and more companies are seeking cyber insurance coverage. The lack of suitable statistical approaches for sco...

Cybersecurity risk has attracted considerable attention in recent decades. However, the modeling of cybersecurity risk is still in its infancy, mainly because of its unique characteristics. In this...

Computing the system signature is an attractive but challenging problem in system reliability. In this article, we propose a novel algorithm to compute the signature of a system with exchangeable c...

Modeling cybersecurity risks is an important, yet challenging, problem. In this paper, we initiate the study of modeling multivariate cybersecurity risks. We develop the first statistical a...

Internet-based computer information systems play critical roles in many aspects of modern society. However, these systems are constantly under cyber attacks that can cause catastrophic consequences. To defend these systems effectively, it is necessary to measure and predict the effectiveness of cyber defense mechanisms. In this article, we investigate how to measure and predict the effectiveness of an important cyber defense mechanism that is known as early-warning. This turns out to be a challenging problem because we must accommodate the dependence among certain four-dimensional time series. In the course of using a dataset to demonstrate the prediction methodology, we discovered a new nonexchangeable and rotationally symmetric dependence structure, which may be of independent value. We propose a new vine copula model to accommodate the newly discovered dependence structure, and show that the new model can predict the effectiveness of early-warning more accurately than the others. We also discus...

Cyber attacks have become a problem that is threatening the economy, human privacy, and even national security. Before we can adequately address the problem, we need to have a crystal clear understanding about cyber attacks from various perspectives. This is a challenge because the Internet is a large-scale complex system with humans in the loop. In this paper, we investigate a particular perspective of the problem, namely the extreme value phenomenon that is exhibited by cyber attack rates, which are the numbers of attacks against a system of interest per time unit. It is important to explore this perspective because understanding the statistical properties of extreme cyber attack rates will pave the way for cost-effective, if not optimal, allocation of resources in real-life cyber defense operations. Specifically, we propose modeling and predicting extreme cyber attack rates via marked point processes, while using the Value-at-Risk as a natural measure of intense cyber attacks. The point process...

In this article, necessary conditions for comparing order statistics from distributions with regularly varying tails are discussed in terms of various stochastic orders. A necessary and sufficient condition for stochastically comparing tail behaviors of order statistics is derived. The main results generalize and recover some results in Kleiber (2002, 2004). Extensions to coherent systems are mentioned as well.

This paper investigates the stochastic comparison of spacings of record values. The likelihood ratio order, the hazard rate order and the mean residual life order between spacings of record values from one sample sequence are developed. Furthermore, the increasing convex order and the mean residual life order between simple spacings of record values from two sample sequences are built as well.

This article deals with the multiple-outlier exponential model. The likelihood ratio order between m-spacings of the combined sample is developed, some results extend the conclusions on simple spacings in Wen et al. (2007).