We develop a “motivic integration” version of the Poisson summation formula for function fields, with values in the Grothendieck ring of definable exponential sums. We also study division algebras over the function field, and show (under some assumptions) that the Fourier transform of a conjugation-invariant test function does not depend on the form of the division algebra. This yields a motivi...

We describe a method to estimate the rate of recombination per generation from the genotypes of a large individual sample of an expanding population, for which the founding event is dated. The approach is illustrated with an application to estimating the major histocompatibility complex (MHC) recombination rate in the Mauritian macaque population. We genotyped 750 macaques by means of 17 micros...

In this paper, a stochastic integral of Ornstein–Uhlenbeck type is represented to be the sum of two independent random variables: one has a tempered stable distribution and the other has a compound Poisson distribution. In distribution, the compound Poisson random variable is equal to the sum of a Poisson-distributed number of positive random variables, which are independent and identically dis...

The theory of formation of an ideal image has been described which shows that the gray level in an image [ollows the Poisson distribution. Based on this concept, various algorithms for object background classification have been developed. Proposed algorithms involve either the maximum entropy principle or the minimum X statistic. The appropriateness of the Poisson distributiou is fun:her streng...

We consider the problem of testing whether a sample of observations comes from a single Poisson distribution. Of particular interest is the alternative that the observations come from Poisson distributions with different parameters. Such a situation would correspond to the frequently discussed situation of overdispersion. We propose a new test for this problem that is based on Anscombe’s varian...

Overview: Categorical Data and Graphics Methods for discrete distributions – testing goodness of fit Hanging rootograms Robust distribution plots Methods for two-way frequency tables – understanding association Fourfold displays Sieve diagrams Mosaic displays and loglinear models for n-way tables Mosaic displays Mosaic matrices Correspondence analysis and MCA Logistic and logit regression Logit...

This paper documents the application of the Conway-Maxwell-Poisson (COM-Poisson) generalized linear model (GLM) for modeling motor vehicle crashes. The COM-Poisson distribution, originally developed in 1962, has recently been re-introduced by statisticians for analyzing count data subjected to over- and under-dispersion. This innovative distribution is an extension of the Poisson distribution. ...

aim : the aim of this study was to compare alternatives methods for analysis of zero inflated count data and compare them with simple count models that are used by researchers frequently for such zero inflated data. background : analysis of viral load and risk factors could predict likelihood of achieving sustain virological response (svr). this information is useful to protect a person from ac...

The interaction of radiation with cells and tissues has a random nature. Therefore, understanding the random nature of cell killing that is determined by Poisson distribution statistics is an essential point in education of radiation biology. RadBioStat is a newly developed educational MATLAB-based software designed for computer-assisted learning of the target theory in radiation biology. Altho...

We develop new probabilistic and deterministic approaches for moment statistics of stochastic partial differential equations with pure jump tempered α-stable (TαS) Lévy processes. With the compound Poisson (CP) approximation or the series representation of the TαS process, we simulate the moment statistics of stochastic reaction-diffusion equations with additive TαS white noises by the probabil...