Copulas are distribution functions with standard uniform univariate marginals. Copulas are widely used for studying dependence among continuously distributed random variables, with applications in finance and quantitative risk management; see, e.g., the pricing of collateralized debt obligations (Hofert and Scherer, Quantitative Finance, 11(5), 775–787,… (More)
Motivated by too restrictive or even incorrect statements about generalized inverses in the literature, properties about these functions are investigated and proven. Examples and counterexamples show the importance of generalized inverses in mathematical theory and its applications.
Several algorithms for sampling exponentially tilted positive stable distributions have recently been suggested. Three of them are known as exact methods, that is, neither do they rely on approximations nor on numerically critical procedures. One of these algorithms is outperformed by another one uniformly over all parameters. The remaining two algorithms… (More)