ERCOT's LOLP is underestimated because it ignores the path reserve level might take over the course of an hour. Some paths reach a reserve level of zero but end up greater than zero. These paths are not included in the LOLP determination even though they would result in a loss of load event...

This paper presents a unified framework for the popular Skewed Generalized t (SGT) distribution and its special cases the Skewed Generalized Error Distribution (SGED), the skewed student's t, the skewed Laplace and skewed normal distributions. The analytical moment equations presented can be...

Given integer-valued and more general real-valued wagers, Feller(1968), Ethier and Khoshnevisan(2002) have established upper and lower bounds on the probability of ruin, which often turn out to be very close to each other. However, the exact calculation of these bounds depends on the unique...

We show a lower bound for the boundary crossing probability [0,1] : h(z) + with a Brownian bridge, a trend function and a boundary function. By that we get also a lower bound for the boundary crossing probability P{∃z ∈ [0,1] : h(z) + Bo(z) u(z)}. It turns out that the bound improves the...

Exact, limiting distributions along with their rates of convergence of exceedance statistics for both order statistics and record statistics are provided when the underlying distribution may have points of discontinuity. Furthermore the exact distribution of record statistics for arbitrary...

A new class of bivariate and trivariate discrete distributions with binomial and multinomial marginals are studied. This class of distributions are obtained by the natural way using probabilistic properties of the considered sampling model. The applications in exceedance models for order...

In this paper, we consider a risk model with two classes of insurance business studied by Yuen[3]. One claim arrival process is a Poisson, process, the other is an Erlang(2) process. With help of a good property of martingales proved in the paper, an Lundberg-like up-bound for the ultimate ruin...

Probabilistic induction allows us to conclude that the probability of a hypothesis being true increases when evidences in favor of the hypothesis occur. A claim made by Karl Popper and David Miller that probabilistic induction is impossible is shown to be untenable, using an example