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Topic: Compound Poisson distribution

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	Springer Online Reference Works
		There are general necessary and sufficient conditions for the convergence of the distribution of sums of independent random variables to a Poisson distribution.
		The Poisson distribution is the limiting case for many discrete distributions such as, for example, the hypergeometric distribution, the negative binomial distribution, the Pólya distribution, and for the distributions arising in problems about the arrangements of particles in cells with a given variation in the parameters.
		The Poisson distribution frequently occurs in queueing theory.
	eom.springer.de /p/p073280.htm (473 words)

	Epidemiologic Perspectives & Innovations \| Full text \| Applying the compound Poisson process model to the reporting of ...
		This paper examines the application of the compound Poisson process model [5-7] to address this issue, emphasizing adjustments to some commonly used interval estimators for rates and rate ratios.
		Assuming that the Poisson distribution is an appropriate model for incident counts, the relevant simulation inputs are the underlying mean incident count λP and the underlying distribution of cases within incidents.
		When the age distributions of the study groups of interest do not depart too greatly from that of the referent population, the simulation results suggest that coverage levels are comparable to those reported earlier for the adjusted confidence intervals for crude rates and rate ratios.
	www.epi-perspectives.com /content/4/1/1 (4644 words)

	Compound Poisson distribution - Wikipedia, the free encyclopedia
		In probability theory, a compound Poisson distribution is the probability distribution of a "Poisson-distributed number" of independent identically-distributed random variables.
		It can be shown that every infinitely divisible probability distribution is a limit of compound Poisson distributions.
		A compound Poisson process with rate λ > 0 and jump size distribution G is a continuous-time stochastic process
	en.wikipedia.org /wiki/Compound_Poisson_distribution (257 words)

	I
		It is an extension of the Poisson Distribution in which the mean of the population is not a constant but varies continuously in a distribution proportional to that of Chi-square.
		The symbol ^ signifies that the Poisson Distribution preceding the symbol ^ is being compounded and the distribution succeeding it, is used as a compounder on the parameter lambda (which equals to the variance and to the mean) of the Poisson Distribution.
		The compounder distribution is not constant, it varies in a rather unpredictable way from steer to steer and within steers, with time post infection (see results tables 3 to 7, pages 28 to 32 and statistical considerations section 4.3.
	www.angelfire.com /vi/vincent/torderweb.html (4674 words)

	Poisson distribution - Wikipedia, the free encyclopedia
		The distribution was discovered by Siméon-Denis Poisson (1781–1840) and published, together with his probability theory, in 1838 in his work Recherches sur la probabilité des jugements en matières criminelles et matière civile ("Research on the Probability of Judgments in Criminal and Civil Matters").
		In Bayesian inference, the conjugate prior for the rate parameter λ of the Poisson distribution is the Gamma distribution.
		The posterior predictive distribution of additional data is a Gamma-Poisson (i.e.
	en.wikipedia.org /wiki/Poisson_distribution (1843 words)

	J. Panaretos : Research And Publications (Site not responding. Last check: )
		"An Elementary Characterisation of the Multinomial and the Multivariate Hypergeometric Distributions"
		"On the Stability of a Characterization of the Poisson Distribution" (1983).
		"On the Stability of a characterisation of the Poisson Distribution" (1985).
	stat-athens.aueb.gr /~jpan/papers.html (1660 words)

	Scientific and Technical Serials Holdings Optimization: A LSU Serials Redesign Project Exercise
		In the biological sciences, the NBD is usually presented in conjunction with the binomial and Poisson distributions (Elliot 1977, 14–66; Williams 1964, 15–16; Bliss 1953, 176–77).
		The geometric distribution is a particular case of the NBD with k=1 (Cooper and Weekes 1983, 137; Haight 1978, 158).
		A Poisson distribution arises from counts of random occurrences happening over time or space at a given rate in a population, and a compound Poisson distribution arises when there is a mixed population of different elements, each having different rates of occurrence distributed according to some function.
	www.lib.lsu.edu /collserv/lrts/ST8.html (985 words)

	BioMed Central \| Full text \| Asymptotic behaviour and optimal word size for exact and approximate word matches between ...
		is a perturbed binomial distribution [12], c is the GC count in w and η is the perturbation parameter of A.
		to a normal distribution, for various word sizes, sequences sizes and number of mismatches, in the case of non-uniform letters distribution, are shown in figure 1.
		to the normal and compound Poisson distribution, in the case of exact word matches, for uniform and non-uniform letters distribution, can be found in [10].
	www.biomedcentral.com /1471-2105/7/S5/S21 (3130 words)

	S Archive: Poisson Gamma Distribution
		The Poison-gamma distribution is a Tweedie distribution with index p between 1 and 2.
		The distribution approaches gamma as p -> 2 and phi * Poisson(mu) as p -> 1.
		Since p = 1 corresponds to Poison and p = 2 corresponds to gamma, the Poison-gamma distribution is genuinely intermediate between the Poisson and gamma distributions.
	www.statsci.org /s/poisgam.html (250 words)

	References (Site not responding. Last check: )
		Proposes a compound Poisson approximation for pattern count on a Markov chain.
		Shows that, as in the order 0 case, the compound Poisson approximation fall in the particular case of the Polya-Aeppli distribution.
		This software allow to compute exact distribution using automatas, but is highly limited both in the Markov model order and in the number of occurrences of the pattern.
	stat.genopole.cnrs.fr /spatt/reference.html (860 words)

	October 15 - Quinn (Site not responding. Last check: )
		where Y is a Poisson random variable with parameter b, and the X_i's are independent identically distributed double truncated Poisson random variables with parameters (N,M) and l, independent of Y.
		The properties of the D compound Poisson distribution are studied.
		A MVUE of the probability function of the D compound Poisson distribution is obtained.
	www.math.mcmaster.ca /rviveros/seminars9798/sem971008.html (274 words)

	STEIN’S METHOD AND APPLICATIONS: A PROGRAM IN HONOR OF CHARLES STEIN - IMS
		The general class can be used to refine the Poisson approximation to a binomial process using probability distributions in contrast to expansions using Stein's method which are typically not approximations by probability distributions.
		The first concerns uniform and non-uniform bounds on the difference between the distribution function of a sum of dependent random variables and the standard normal distribution function.
		We show the asymptotic Wigner distribution of eigenvalues of random matrices distributed according to a martingale type stochastic model for the coefficients, which includes the Wigner-Ensemble.
	www.ims.nus.edu.sg /Programs/stein/abstracts.htm (2345 words)

	[No title]
		Let the size of a PARTICULAR claim in the first group have the uniform distribution on [0,2], in the second group — the exponential distribution with an expected value of 2, in the third — always equal 3.
		The flow of claims arriving at an insurance company may be represented as a compound Poisson process.
		Let the amount of a particular claim is exponentially distributed with a mean of 2.
	www-rohan.sdsu.edu /~rotar/575-02-f.doc (813 words)

	f79ag
		Models for claim numbers: the Poisson distribution, the negative binomial distribution.
		Models for aggregate claims: the compound Poisson distribution, the individual risk model.
		Use the compound Poisson distribution to describe aggregate claims.
	www.ma.hw.ac.uk /ams/teach/modules0405/f79ag (407 words)

	[No title] (Site not responding. Last check: )
		The methods of computing premiums are based on statistical data on the parameters of the distribution of S. To be of practical use, a method of premium computation must be simple.
		It is natural to model S as a mixture of the deterministic claim of size Pr(S = 373,000) = p and a compound Poisson sum from the previous analysis with probability 1-p.
		Even if N is Poisson, equation (2) can be solved explicitly only in very special cases.
	math.uc.edu /~brycw/classes/576/lect10.htm (2216 words)

	Statistical Modelling library for S-Plus
		Density, distribution function and random deviates for the inverse Gaussian distribution.
		Density and distribution function for the Poisson gamma (or compound Poisson) distribution.
		The Digamma distribution is the unit deviance distribution for the gamma family.
	www.statsci.org /s/index.html (466 words)

	Jan Dhaene
		DHAENE J. "Approximating the compound negative binomial distribution by the compound Poisson distribution", Bulletin of the Swiss Association of Actuaries, 1991 (1), 117-121.
		DE PRIL N., DHAENE J. "Error bounds for compound Poisson approximations of the individual risk model", ASTIN Bulletin, 22 (2), 135-148.
		GOOVAERTS M.J., DHAENE J. "The compound Poisson approximation for a portfolio of dependent risks", Insurance : Mathematics and Economics, 18 (1), 81-85.
	www.vacs.be /jan_dhaene.htm (1009 words)

	Notes by Prapun Suksompong - Prapun's Notes on Probability
		Poisson distribution, Convergence to the Poisson Law, Compound Poisson Distribution, Random Sum and Filtered Process, Exponential Distribution, Homogeneous Poisson Process (HPP), Non-homogeneous Poisson Process (NHPP), Poisson Limit for Superposition of Processes, Filtered Poisson Process (FPP), Poisson Approximation in Total Variation distance and Relative Entropy, Poisson Limit for Superposition of Processes, Poisson Process in General Space.
		Interestingly, given a specific average, the estimated variance is not only nonnegative, but it is also lower-bounded by a nonnegative function of the average which is strictly positive almost everywhere.
		In fact, most of the standard probability distributions can be characterized as being maximum entropy distributions under appropriate moment constraints.
	prapun.googlepages.com (372 words)

	Welcome!
		Huang, M.L. and Fung, K.Y. On Moments and Cumulants of the D Compound Poisson Distribution, Statistical Papers,Volume 38, Number 3, pp.357-361, 1997.
		Huang, M.L. and Fung, K.Y. The D Compound Poisson Distribution, Statistische Hefte, Volume 34, pp.319-338, 1993.
		Huang, M.L. and Fung, K.Y. The D Distribution and its Applications, Statistische Hefte, Volume 34, pp.143-159, 1993.
	spartan.ac.brocku.ca /~mhuang/publication.html (475 words)

	Math-544
		the evaluation of risk, types of insurance, distributions of possible damages (in the case of casualty insurance) and human lifetimes (in the case of life insurance), principles used by insurance companies in managing their activities.
		A slight change of the order of exposition and even of the contents is also possible.
		The flow of claims, compound Poisson process, some more general schemes.
	www-rohan.sdsu.edu /~rotar/575-03.html (152 words)

	Statistical Laboratory Seminars - Michaelmas Term 2000
		Secondly, a new construction will be given which allows to define a rigorous Feynman integral for very general Schroedinger equations including the cases of singular potentials and magnetic fields.
		The compound Poisson distribution associated with a distribution P on the real line and some λ >0 is defined to be the distribution of Y=X
		In this talk, I will describe the formulation of a time- and cohort-stratified model of the transmission dynamics of vCJD, which relates estimates of the numbers of BSE-infected cattle that entered the human food supply to the cases of vCJD which have arisen to date.
	www.statslab.cam.ac.uk /Seminars/statsemmich2000.html (923 words)

	Estimating Stein's constants for compound Poisson approximation
		Stein's method for compound Poisson approximation was introduced by Barbour, Chen and Loh.
		One difficulty in applying the method is that the bounds on the solutions of the Stein equation are by no means as good as for Poisson approximation.
		We show that, for the Kolmogorov metric and under a condition on the parameters of the approximating compound Poisson distribution, bounds comparable with those obtained for the Poisson distribution can be recovered.
	projecteuclid.org /DPubS?service=UI&version=1.0&verb=Display&handle=euclid.bj/1081449593 (210 words)

	Inaugural Article: Distributional regimes for the number of k-word matches between two random sequences -- Lippert et ...
		Inaugural Article: Distributional regimes for the number of k-word matches between two random sequences -- Lippert et al.
		Distributional regimes for the number of k-word matches between two random sequences
		normal distribution arises when the word size is small and matches
	www.pnas.org /cgi/content/abstract/99/22/13980 (325 words)

	Geiringer Mathematical Theory of Probability and Statistics
		Gaussian Distribution, Poisson Distribution (Sections 5 and 6)
		Limit Distribution of the Sum of INdependent Discrete Random Variables (Sections 3 and 4)
		Distribution of the Correlation Coefficient (Sections 4 and 5)
	www.agnesscott.edu /Lriddle/women/abstracts/geiringer_probability.htm (424 words)

	The Stuttering Generalized Waring Distribution - Munich RePEc Personal Archive
		Panaretos, John and Xekalaki, Evdokia (1986): The Stuttering Generalized Waring Distribution.
		The stuttering generalized Waring distribution is introduced and shown to arise through two urn genesis schemes.
		Reproduction and distribution subject to the approval of the copyright owners.
	mpra.ub.uni-muenchen.de /6250 (108 words)

	Representative Publications (Site not responding. Last check: )
		Huang, M.L. and Fung, K.Y. "On Moments and Cumulants of the D Compound Poisson
		Distribution", Statistical Paper, Volume 38, Number 3, pp.357-361, 1997.
		Huang, M.L. and Fung, K.Y. "The D Compound Poisson Distribution", Statistische Hefte,
	www.brocku.ca /mathematics/people/huang/spartan/publications.phtml (277 words)

	Gamze Özel's Home Page
		Özel, G., İnal, C., The probability function of the compound Poisson distribution using integer partitions and Ferrer's Graph, Bulletin of Statistics and Economics, Spring Vol.
		Compound Poisson Distribution and It's Properties, 18 May 2006, H.U. Department of statistics.
		Özel, G. İnal, C., Cumulative Distribution of First Exit Time for a Compound Poisson Process, 56 th Session of ISI, 22-29 August 2007, Lisbon, Portugal.
	yunus.hacettepe.edu.tr /~gamzeozl (215 words)

	Non-Uniform Random Variate Generation
		Generating order statistics with distribution function F. Generating exponential random variates in batches.
		Generating random vectors uniformly distributed on $C sub d$.
		Tsang, W.W. Tucker, A.C. Tukey's lambda distribution 482
	cg.scs.carleton.ca /~luc/rnbookindex.html (1952 words)

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