A zero-inflated Poisson (ZIP) distribution is commonly used for modelling process data with single type of defect, and developing appropriate tools instituting statistical control manufacturing processes. However, in reality, such scenarios are very common where more than one defect can occur. For example, occurrences defects like solder short circuits (shorts) absence (skips) on printed circui...

Queueing systems which map Poisson input processes to Poisson output processes have been well-studied in classical queueing theory. This paper considers two discretetime queues whose analogs in continuous-time possess the Poisson-in-Poisson-out property. It is shown that when packets arriving according to an arbitrary ergodic stationary arrival process are passed through these queueing systems,...

We consider a point process i + ξi, where i ∈ Z and the ξi’s are i.i.d. random variables with variance σ. This process, with a suitable rescaling of the distribution of ξi’s, converges to the Poisson process in total variation for large σ. We then study a simple queueing system with our process as arrival process, and we provide a complete analytical description of the system. Although the arri...

We construct superefficient estimators of Stein type for the intensity parameter λ > 0 of a Poisson process, using integration by parts and superharmonic functionals on the Poisson space.

This note concerns stochastic processes on chains of arbitrary length whose Poisson kernel can be expressed in terms of the q-Racah polynomials, the most general q-deformed orthogonal polynomials in the discrete series of the Askey scheme. We give a new interpretation of this kernel as the probability transition density for a subordinated Markov process with only nearest neighbor hops. As an ap...

We show that the stick-breaking construction of the beta process due to Paisley et al. (2010) can be obtained from the characterization of the beta process as a Poisson process. Specifically, we show that the mean measure of the underlying Poisson process is equal to that of the beta process. We use this underlying representation to derive error bounds on truncated beta processes that are tight...

Numerical simulations of hierarchical gravitational clustering in an expanding universe show that, as time evolves, small clusters merge with each other to form larger clusters, whereas fragmentation of clusters is relatively uncommon. Stochastic models of the hierarchical clustering process can provide insight into, as well as useful approximations to, the evolution measured in these simulatio...

Motivated by non-Poisson stochastic variability found in service system arrival data, we extend established service system staffing algorithms using the square-root staffing formula to allow for non-Poisson arrival processes. We develop a general model of the non-Poisson nonstationary arrival process that includes as a special case the nonstationary Cox process (a modification of a Poisson proc...

Corollary 1.1. Consider an M/M/s queue with Poisson(λ ) arrivals and each server having exponential service time exp(μ) service. If λ > sμ , then the output process in steady state is Poisson(λ ). Proof. Let X(t) denote the number of customers in the system at time t. Since M/M/s process is a birth and death process, it follows from the previous proposition that {X(t), t ≥ 0} is time reversible...