Conditional Exceedance Probabilities

Exceedance probabilities for parametric control charts

Common control charts assume normality and known parameters. Quite often these assumptions are not valid and large relative errors result in the usual performance characteristics, such as the false alarm rate or the average run length. A fully nonparametric approach can form an attractive alternative but requires more Phase I observations than are usually available. Sufficiently large parametri...

Exceedance Probabilities for the Dirichlet Distribution

We derive an efficient method to calculate exceedance probabilities (EP) for the Dirichlet distribution when the number of event types is larger than two. Also, we present an intuitive application of Dirichlet EPs and compare our method to a sampling approach which is the current practice in neuroimaging model selection.

Accelerated Monte Carlo estimation of exceedance probabilities under monotonicity constraints

— The problem of estimating the probability p = P (g(X) ≤ 0) is considered when X represents a multivariate stochastic input of a monotonic function g. First, a heuristic method to bound p, originally proposed by de Rocquigny (2009), is formally described, involving a specialized design of numerical experiments. Then a statistical estimation of p is considered based on a sequential stochastic e...

Rapidly bounding the exceedance probabilities of high aggregate losses

We consider the task of assessing the righthand tail of an insurer’s loss distribution for some specified period, such as a year. We present and analyse six different approaches: four upper bounds, and two approximations. We examine these approaches under a variety of conditions, using a large event loss table for US hurricanes. For its combination of tightness and computational speed, we favou...

Quantum Conditional Probabilities Are Not Probabilities of Quantum Conditional