Measuring Risk Dependencies Due to Two Natural Disasters by Bivariate Copula Plamena Zlateva 1 and Dimiter Velev 2 + 1 Institute of System Engineering and Robotics - BAS, Sofia, Bulgaria 2 University of National and World Economy, Sofia, Bulgaria Abstract. The bivariate copula potentiality for measuring risk dependencies due to occurrence of two natural disasters is presented. Some bivariate copula essentials are described. Several copula dependence measures (concordance, Kendall’s tau, Spearman’s rho, positively quadrant dependent, tail dependence) are considered. The results about the measuring risk dependencies can support the stakeholders to take more informed decisions regarding the efficient allocation of the available funding for the improvement of risk management with respect to natural disasters. A concept for implementing the bivariate copula models as a part of a Web integrated information system for risk management of natural disasters is outlined. Keywords: bivariate copula, risk dependencies, Kendall’s tau, Spearman’s rho, natural disasters 1. Introduction Today it is recorded an increase in negative severities of natural disasters on the life quality compared to previous years [1]. Billions of dollars cost annual losses resulting from floods, hurricanes, earthquakes, tornadoes, landslides etc. Unfortunately, natural disasters are impossible to avoid and infrastructure systems cannot be made totally invulnerable. The only feasible strategies for risk management and consequences reduction can be designed [2, 3]. For these reasons, the numerous scientific and applied investigations are conducted on separate natural disaster and their consequences for the people’s health and property, the environment, cultural and material assets. The scientific activities are concerned to the development and application of modern methods and tools for analysis and estimation of risk events; development of models for risk control in emergency situations; development and maintenance of dedicated databases and information systems. It is important to note that mostly the interdependence of natural disasters and their joint impact on society and infrastructure are not sufficiently taken into account in scientific study. Therefore it is necessary to propound varied mathematical methods for measuring risk dependencies due to natural disasters. One method of modelling risk dependencies which has become very popular recently is the copula [4, 5]. The word copula is a Latin noun which means ‘a link, tie or bond’, and was first employed in a mathematical or statistical sense by Abe Sklar. Mathematically, a copula is a function which allows us to combine univariate distributions to obtain a joint distribution with a particular dependence structure [6]. The copulas provide full information on the dependency structure between risks. The concept of copulas is based on separating the joint marginal distribution function into a part that describes the dependence structure and multiple parts that describe the marginal distribution functions [7-9]. The purpose of the paper is to present the bivariate copula potentiality for measuring risk dependencies due to occurrence of two natural disasters. The described bivariate copula elements are envisaged to be implemented as a part of a Web integrated information system for risk management of natural disasters. 2. Bivariate Copula Essentials The 2-dimensional copula links the bivariate cumulative distribution function to its one-dimensional marginals cumulative distribution function and therefore, it carries the dependence structure between these + Corresponding author. Tel.: + 359 2 8195 694; fax: +359 2 962 39 03. E-mail address: dvelev@unwe.acad.bg. 182