The path to copulas is paved (also) with shock models

Any stochastic dependence can be modeled using copulas according to the Sklar's theorem (1959) . Copulas arising from shock models have started in 1967 by Marshall and Olkin with one of the most cited papers in the area. A major step forward was done in 1996 by Marshall and the next major step in 2015 by Durante, Girard and Mazo. They introduced a general framework in a form of a stochastic model that includes most of the shock based models. Numerous applications of these models have been found during this half-a-century including applications in life sciences. In our talk some newly developed classes of copulas of the kind will be presented, including maxmin copulas and reflected maxmin copulas, together with some properties and applications. The surprising fact about these new copulas is that they may be non-singuar as opposed to the usual Marshall type copulas. The Slovene group concentrated at IMFM, has emerged in only two years at the cutting edge in this area of mathematical statistics with 10 presentations at international conferences (two invited plenary  talks) and international cooperation established with 5 European and Canadian universities.