We consider compound geometric approximation for a nonnegative, integervalued random variable W . The bound we give is straightforward but relies on having a lower bound on the failure rate of W . Applications are presented to M/G/1 queuing systems, for which we state explicit bounds in approximations for the number of customers in the system and the number of customers served during a busy per...

Multiple orthogonal polynomials are polynomials of one variable that satisfy orthogonality conditions with respect to several measures. They are a very useful extension of orthogonal polynomials and recently received renewed interest because tools have become available to investigate their asymptotic behavior. They appear in rational approximation, number theory, random matrices, integrable sys...

We investigate the probability that a sample Γ = (Γ1,Γ2, . . . ,Γn) of independent, identically distributed random variables with a geometric distribution has no elements occurring exactly j times, where j belongs to a specified finite ‘forbidden set’ A of multiplicities. Specific choices of the set A enable one to determine the asymptotic probabilities that such a sample has no variable occuri...

If a population is growing in a randomly varying environment, such that the finite rate of increase per generation is a random variable with no serial autocorrelation, the logarithm of population size at any time t is normally distributed. Even though the expectation of population size may grow infinitely large with time, the probability of extinction may approach unity, owing to the difference...

This paper addresses the problem of human pose estimation, given images taken from multiple dynamic but calibrated cameras. We consider solving this task using a part-based model and focus on the part appearance component of such a model. We use a random forest classifier to capture the variation in appearance of body parts in 2D images. The result of these 2D part detectors are then aggregated...