Com Poisson distribution is capable of modeling the count responses irrespective of their mean variance relation and the parameters of this distribution when fitted to a simple cross sectional data can be efficiently estimated using maximum likelihood (ML) method. In the regression setup, however, ML estimation of the parameters of the Com Poisson based generalized linear model is computational...

Germ-cell mutations may occur during meiosis, giving rise to independent mutant gametes in a Poisson process, or before meiosis, giving rise to multiple copies of identical mutant gametes at a much higher probability than the Poisson expectation. We report that the occurrence of these early premeiotic clusters of new identical mutant alleles increases the variance-to-mean ratio of mutation rate...

Noise is present in all image sensor data. Poisson distribution is said to model the stochastic nature of the photon arrival process, while it is common to approximate readout/thermal noise by additive white Gaussian noise (AWGN). Other sources of signal-dependent noise such as Fano and quantization also contribute to the overall noise profile. Question remains, however, about how best to model...

The behavior and performance of denoising algorithms are governed by one or several parameters, whose optimal settings depend on the content of the processed image and the characteristics of the noise, and are generally designed to minimize the mean squared error (MSE) between the denoised image returned by the algorithm and a virtual ground truth. In this paper, we introduce a new Poisson-Gaus...

Generalized estimating equations (GEE) fit parameters based on sums of weighted residuals, which may be applied for example to the Poisson distribution. We discuss Generalized Poisson (GP) response data. This distribution has a more flexible variance function than the Poisson distribution and has an additional dispersion parameter. To fit this parameter, second level estimating equations based ...

We study a queueing system having a mixture of a special semi-Markov process (SSMP) and a Poisson process as the arrival process, where the Poisson arrival is regarded as interfering traffic. It is shown by numerical examples that the SSMP customers receive worse treatment than Poisson customers, i.e., the mean waiting time of SSMP customers is longer than that of Poisson customers. We also pro...

It is well known that the vertex number of the typical cell of a stationary hyperplane tessellation in R has, under some mild conditions, an expectation equal to 2, independent of the underlying distribution. The variance of this vertex number can vary widely. Under Poisson assumptions, we give sharp bounds for this variance, showing, in particular, that its maximum is attained if and only if t...

We show that, for a stationary version of Hammersley’s process, with Poisson sources on the positive x-axis and Poisson sinks on the positive y-axis, the variance of the length of a longest weakly North–East path L(t, t) from (0,0) to (t, t) is equal to 2E(t −X(t))+, where X(t) is the location of a second class particle at time t . This implies that both E(t −X(t))+ and the variance of L(t, t) ...

In many contexts, such as queueing theory, spatial statistics, geostatistics and meteorology, data are observed at irregular spatial positions. One model of this situation is to consider the observation points as generated by a Poisson Process. Under this assumption, we study the limit behavior of the partial sums of the Marked Point Process {(ti, X(ti))}, where X(t) is a stationary random fiel...

Introduction Spatial Scan Statistics [1] usually assume Poisson or Binomial distributed data, which is not adequate in many disease surveillance scenarios. For example, small areas distant from hospitals may exhibit a smaller number of cases than expected in those simple models. Also, underreporting may occur in underdeveloped regions, due to inefficient data collection or the difficulty to acc...