C-control chart assumes that process nonconformities follow a Poisson distribution. In actuality, however, this Poisson distribution does not always occur. A process control for semiconductor based on a Poisson distribution always underestimates the true average amount of nonconformities and the process variance. Quality is described more accurately if a compound Poisson process is used for pro...

We consider a stochastic fluid network where the external input processes are compound Poisson with heavy-tailed Weibullian jumps. Our results comprise of large deviations estimates for buffer content process in vector-valued Skorokhod space which is endowed product $$J_1$$ topology. To illustrate our framework, we provide explicit tandem queue. At heart proof recent sample-path result, and nov...

We consider in this paper the optimal dividend problem for an insurance company whose uncontrolled reserve process evolves as a classical Cramér–Lundberg model with arbitrary claim-size distribution. Our objective is to find the dividend payment policy which maximizes the cumulative expected discounted dividend pay-outs until the time of bankruptcy imposing a ceiling on the dividend rates. We c...

In 1986, Merzbach and Nualart demonstrated a method of transforming a two-parameter point process into a planar Poisson process of unit rate, using random stopping sets. Merzbach and Nualart's theorem applies only to a special class of point processes, since it requires two restrictive conditions: the (F4) condition of conditional independence and the convexity of the 1-compensator. The (F4) co...

We consider the problem of testing two simple hypotheses about unknown local characteristics of several independent Brownian motions and compound Poisson processes. All of the processes may be observed simultaneously as long as desired before a final choice between hypotheses is made. The objective is to find a decision rule that identifies the correct hypothesis and strikes the optimal balance...

This article considers the problem of evaluating infinite-time (or finite-time) ruin probability under a given compound Poisson surplus process. By approximating the claim size distribution by a finite mixture exponential, say Hyperexponential, distribution. It restates the infinite-time (or finitetime) ruin probability as a solvable ordinary differential equation (or a partial differential equ...

In this paper we extend Rydberg-Shephard’s activity, direction and size decomposition of trade-by-trade price movements to the multivariate case. We illustrate our ideas using a bivariate modelling problem — modelling the evolution of the prices of Ford and GM shares. Throughout we use the continuous record of trades made in the first five months of 1997 on the New York Stock Exchange (NYSE).

Model-based collaborative filtering (CF) analyzes user–item interactions to infer latent factors that represent user preferences and item characteristics in order to predict future interactions. Most CF approaches assume that these latent factors are static; however, in most CF data, user preferences and item perceptions drift over time. Here, we propose a new conjugate and numerically stable d...

Biological dosimetry based on chromosome aberration scoring in peripheral blood lymphocytes enables timely assessment of the ionizing radiation dose absorbed by an individual. Here, new Bayesian-type count data inverse regression methods are introduced for situations where responses are Poisson or two-parameter compound Poisson distributed. Our Poisson models are calculated in a closed form, by...