We provide evidence suggesting that the assumption on the probability distribution for return innovations is more influential for Value at Risk (VaR) performance than the conditional volatility specification. We also show that some recently proposed asymmetric probability distributions and the...

The skewness of a statistical distribution is often used to determine whether that distribution is symmetric or not. Such a determination is misleading. To show this we have analyzed a broad range of (classes of) skewness measures – complying with the requirements of a general skewness measure...

This paper studies the approximation of extreme quantiles of random sums of heavy-tailed random variables. A key application of this approximation is the calculation of operational VaR (value at risk) for financial institutions. The paper follows work by Böcker & Klüppelberg (2005) & Böcker...

In this paper, we consider a continuous time risk process for which the claim number process extends the classical Poisson process, and the claim sizes are independent, Erlang random variables, but not necessarily identically distributed. For this process, we obtain recursive formulas that allow...

The weighted Weibull model is proposed following the method of Azzalini (1985). Basic properties of the distribution; including moments, generating function, hazard rate function and estimation of parameters; have been studied

Health-service users err in posttest probability evaluations. Here we document for the first time that they succeed when they reason about numbers of cases and make distributive evaluations. A sample of women interested in prenatal testing incorrectly evaluated the posttest probability that a...

New results on conditional joint probability distributions of first exit times are presented for a continuous-time stochastic process defined as the mixture of Markov jump processes moving at different speeds on the same finite state space, while the mixture occurs at a random time. Such mixture...