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Topic: Poisson process

Related Topics

Levy process

Poisson distribution

Compound Poisson distribution

Compound Poisson process

Exponential distribution

Gamma distribution

Stochastic process

Expected value

Branching process

Poisson manifold

Erlang distribution

Probability density function

Normal distribution

Beta distribution

Central limit theorem

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	Poisson process - Wikipedia, the free encyclopedia
		The Poisson process is a continuous-time process; its discrete-time counterpart is the Bernoulli process.
		A Poisson process is a pure-birth process, the simplest example of a birth-death process.
		Just as a Poisson random variable is characterized by its scalar parameter λ, a homogeneous Poisson process is characterized by its rate parameter λ, which is the expected number of "events" or "arrivals" that occur per unit time.
	en.wikipedia.org /wiki/Poisson_process (868 words)

	UOR_2.13
		The Poisson process is one example of a "point process" in which discrete events (arrivals) occur at particular points in time.
		Maintaining the depiction of a stochastic process at such a general level, although fine in theory, yields an intractable model and one for which the data (to estimate all the joint pdf 's) are virtually impossible to obtain.
		The Poisson process is a special case of a renewal process, being the only continuous-time renewal process having "no memory." However, the kind of process we are considering can exhibit both memory and dependence among the inter-event times.
	web.mit.edu /urban_or_book/www/book/chapter2/2.13.html (1512 words)

	Stochastic Processes and Queuing Models, Queueing Theory - Numericana
		Simulating a poisson process is easy with a uniform random number generator.
		For such a process, a generator matrix Q is defined (also called a transition rate matrix) as the time derivative of the stochastic matrix that gives the probability of ending up in state j at time t, starting from state i at time 0.
		The very definition of the activity of a stochastic process makes it clear that when several Poisson processes are so combined, the resulting process is a process whose activity is the sum of the activities of the component processes.
	home.att.net /~numericana/answer/stochastic.htm (1774 words)

	Poisson Distribution (via CobWeb/3.1 planetlab2.isi.jhu.edu) (Site not responding. Last check: 2007-10-13)
		Other phenomena that often follow a poisson distribution are death of infants, the number of misprints in a book, the number of customers arriving, and the number of activations of a geiger counter.
		The poisson distribution was derived by the french mathematician Poisson in 1837, and the first application was the describtion of the number of death by horse kicking in the prussian army (Bortkiewicz, 1898).
		Thus, the poisson distribution is cheaper to use because the number of accidents is usually recorded by the police department, whereas the total number of drivers is not.
	huizen.dds.nl.cob-web.org:8888 /~berrie/poisson.html (324 words)

	Poisson distribution - Wikipedia, the free encyclopedia (via CobWeb/3.1 planetlab2.isi.jhu.edu) (Site not responding. Last check: 2007-10-13)
		Albert Einstein used Poisson noise to show that matter was composed of discrete atoms and to estimate Avogadro's number; he also used Poisson noise in treating flbody radiation to demonstrate that electromagnetic radiation was composed of discrete photons.
		The Poisson distribution can be derived as a limiting case to the binomial distribution as the number of trials goes to infinity and the expected number of successes remains fixed.
		For temporally distributed events, the Poisson distribution is the probability distribution of the number of events that would occur within a preset time, the Erlang distribution is the probability distribution of the amount of time until the nth event.
	en.wikipedia.org.cob-web.org:8888 /wiki/Poisson_distribution (1853 words)

	CHU - Motivating the Poisson Process in Queuing Models.
		Another example is Schmuland (2001), who uses the Poisson model to explain the phenomena of bursts in shark attacks and the scoring patterns of ice hockey legend Wayne Gretzky.
		Based on his observation that the Poisson distribution provides a good fit for goals scored in ice hockey games, Berry (2000) assumes an exponential distribution for the times between goals to estimate the strategic time to “pull the goalie” when a team is down in a game.
		One property of the Poisson process is that the number of events within alternative time intervals is also Poisson but with a proportionally adjusted mean.
	ite.pubs.informs.org /Vol3No2/Chu/index.php (2484 words)

	Epsilon-Delta » The Poisson Process in Computing (via CobWeb/3.1 planetlab2.isi.jhu.edu) (Site not responding. Last check: 2007-10-13)
		The Poisson process is used in the study of telecom networks, where there are finitely many circuits to connect customers and calls come in as a stochastic process.
		This seems to hurt the case for the Poisson process in IT, but often what happens is that we take chunks of time over which arrival rates are somewhat constant, and model them as separate Poisson processes.
		The Poisson process does a fairly good job of modeling telecommunications and data networking problems, so it’s reasonable to use it to solve problems.
	epsilondelta.net.cob-web.org:8888 /2006/07/13/the-poisson-process-in-computing (798 words)

	The Poisson Process
		The Poisson process is one of the most important random processes in probability theory.
		It is widely used to model random "points" in time and space, such as the times of radioactive emissions, the arrival times of customers at a service center, and the positions of flaws in a piece of material.
		The process has a beautiful mathematical structure, and is used as a foundation for building a number of other, more complicated random processes.
	www.math.uah.edu /stat/poisson (94 words)

	PlanetMath: Poisson process
		Condition 4 says that the event occurs more than once is very unlikely (the rate approaches zero as the time interval shrinks to zero).
		Cross-references: stochastic process, Poisson distribution, interval, event, terms, constant, O notation, stationary independent increments, counting process
		This is version 5 of Poisson process, born on 2005-02-09, modified 2006-10-04.
	planetmath.org /encyclopedia/PoissonProcess.html (132 words)

	[ns] Poisson process
		Jing Saikat Ray wrote: If you observe a random process for a time period 'T', and the number of arrivals during this period happen to have the same mean and variance, you CANNOT conclude that the process is a Poisson Process.
		However, if X(t) and Y(t) are two independent Poisson Processes and X1(t) is created from X(t) by sending an arrival at X to X1 with probability 'p1', and similarly for Y1(t); both X1(t) and Y1(t) are Poisson processes on their own right and since X(t) and Y(t) were independent, so are X1(t) and Y1(t).
		However, if X(t) and Y(t) are two independent Poisson Processes and X1(t) is created from X(t) by sending an arrival at X to X1 with probability 'p1', and similarly for Y1(t); both X1(t) and Y1(t) are Poisson processes on their own right and since X(t) and Y(t) were independent, so are X1(t) and Y1(t).
	mailman.isi.edu /pipermail/ns-users/2004-January/038411.html (1162 words)

	Counting Process (Site not responding. Last check: 2007-10-13)
		Such a process is right continuous, as indicated by the graph in Fig.
		As it is often case in the theory of stochastic processes, we assume that the
		For an inhomogeneous process, the procedures 1 and 2 can be modified using the appropriate theory of inhomegeneous Poisson process.
	robotics.caltech.edu /~zoran/Research/poisson/node1.html (927 words)

	Handout on Poisson process (via CobWeb/3.1 planetlab2.isi.jhu.edu) (Site not responding. Last check: 2007-10-13)
		Handout on the Poisson process and the queuing theory.
		Explain how you understand the notions of the stationary regime, the stationary distribution, the behavior of the process in the long run.
		Military vehicles arrive at a service facility according to the Poisson process.
	www-rohan.sdsu.edu.cob-web.org:8888 /~rotar/550-h-poisson-process.html (261 words)

	A Compound Poisson Process for Relaxing the Molecular Clock -- Huelsenbeck et al. 154 (4): 1879 -- Genetics
		The compound Poisson process discussed in this article places events of substitution-rate change on the tree according to a Poisson process.
		In this example, which illustrates the process for the tree from Fig 1, three events of substitution-rate change occur.
		process with exponential priors of means 1 and 10 (Fig 11).
	www.genetics.org /cgi/content/full/154/4/1879 (5893 words)

	Splitting a Poisson Process
		Suppose that each arrival in the Poisson process, independently, is of one of two types: type 1 with probability
		For example, suppose that the arrivals are radioactive emissions and that each emitted particle is either detected (type 1) or missed (type 0) by a counter.
		Suppose that each arrival in the Poisson process, independently, is of one of
	www.ds.unifi.it /VL/VL_EN/poisson/poisson5.html (518 words)

	Poisson process via independence assumptions I (Site not responding. Last check: 2007-10-13)
		Suppose that instead of making specific assumptions about the inter-arrival distributions, suppose we make assumptions about the behavior of the counting process itself.
		We can then define a Poisson process to be a counting process which has stationary, independent increments and for which
		This is a more useful approach since it makes no specific assumptions about probability distributions, only how the increments relate to one another, and assumptions about (probabalistically) how fast the process changes states.
	www.uwm.edu /~ericskey/571F99/L05/node2.html (228 words)

	8.1.7.2. Non-Homogeneous Poisson Process (NHPP) - power law
		Probabilities of a given number of failures for the NHPP model are calculated by a straightforward generalization of the formulas for the HPP.
		The time to the first fail for a Power Law process has a Weibull distribution with shape parameter b and characteristic life a.
		This name is confusing and should be avoided, however, since it mixes a life distribution model applicable to the lifetimes of a non-repairable population with a model for the inter-arrival times of failures of a repairable population.
	www.itl.nist.gov /div898/handbook/apr/section1/apr172.htm (438 words)

	Poisson Process (Site not responding. Last check: 2007-10-13)
		The number of vehicles passing the point A in an hour follows the Poisson distribution with mean 60; 20% of these vehicles are trucks.
		The number of vehicles passing B in an hour is also Poisson with mean 80; 30% of these are trucks.
		So, for this reason we only compute the arrival of vehicles, and considering the number of passenger for each type of vehicle we can compute the expected value of, say Z, the number of people who go to the restaurant.
	www.physicsforums.com /showthread.php?t=65923 (519 words)

	Poisson Processes and Queues (via CobWeb/3.1 planetlab2.isi.jhu.edu) (Site not responding. Last check: 2007-10-13)
		The occurrences of a sequence of discrete events can often be realistically modeled as a Poisson process. The defining characteristic of such a process is that the time intervals between successive events are exponentially distributed. Given a sequence of discrete events occurring at times t
		is exponential for all n. It's convenient to represent a simple Poisson process schematically as shown below.
		This is the probability distribution for a simple Poisson "counting" process, representing the probability that exactly n events will have occurred by the time t. Obviously the sum of these probabilities for n = 1 to ¥ equals 1, because the the exponential e
	www.mathpages.com.cob-web.org:8888 /home/kmath026/kmath026.htm (1010 words)

	Process for Organization of Internet Standards ONg (poisson) Charter
		POISSON is concerned with documenting issues relevant to the IETF process.
		The tricky part of describing the IETF process, certainly in the fast changing world of the Internet, is that when you describe the process in too much detail, the IETF loses its flexibility, when you describe to little it becomes unmanageable.
		Last but not least, Poisson will serve as a generic platform where the IAB and IESG can discuss policy questions if there is the need for consensus polling.
	www.ietf.org /html.charters/OLD/poisson-charter.html (558 words)

	Compound Poisson process approximation, A. D. Barbour, Marianne Månsson
		Compound Poisson process approximation, A. Barbour, Marianne Månsson
		Compound Poisson processes are often useful as approximate models, when describing the occurrence of rare events.
		Our approach is to use Stein's method directly, rather than by way of declumping and a marked Poisson process; this has conceptual advantages, but entails technical difficulties.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.aop/1029867135 (224 words)

	The Poisson point process
		The Poisson process was discovered by Simeon-Denis Poisson (1781-1840) and describes a statistic point process of single events which occur ramdom in time.
		An example for a possion process is the decay of some types of radioactive isotopes.
		The observed interspike-interval-distribution [4] looks like the exponential interevent-distribution (the interevent-distribution defines the propability of the time-interval-length between two events) of the Poisson process.
	www.neuro.uni-bremen.de /~dip/poissonprocess.html (229 words)

	Stat 433: Chapter V.2: Poisson point process (Site not responding. Last check: 2007-10-13)
		Poisson process: collection of random variables indexed by time
		Poisson point process: collection of random variables indexed by intervals
		KEY POINT: No mention of "Poisson" anywhere in definition
	gosset.wharton.upenn.edu /~foster/teaching/433/class_poisson_3.html (124 words)

	Poisson Process -- from Wolfram MathWorld (via CobWeb/3.1 planetlab2.isi.jhu.edu) (Site not responding. Last check: 2007-10-13)
		A Poisson process is a process satisfying the following properties:
		In the limit of the number of trials becoming large, the resulting distribution is called a Poisson distribution.
		Papoulis, A. Probability, Random Variables, and Stochastic Processes, 2nd ed.
	mathworld.wolfram.com.cob-web.org:8888 /PoissonProcess.html (120 words)

	Create Poisson process... (Site not responding. Last check: 2007-10-13)
		A command to create a PointProcess object that represents a Poisson process.
		A Poisson process is a stationary point process with a fixed density
		First, the number of points N in the time domain is determined.
	www.fon.hum.uva.nl /praat/manual/Create_Poisson_process___.html (69 words)

	8.1.7.1. Homogeneous Poisson Process (HPP)
		This model comes about when the interarrival times between failures are independent and identically distributed according to the exponential distribution, with parameter
		This basic model is also known as a Homogeneous Poisson Process (HPP).
		Planning reliability assessment tests (under the HPP assumption) is covered in a later section, as is estimating the MTBF from system failure data and calculating upper and lower confidence limits.
	www.itl.nist.gov /div898/handbook/apr/section1/apr171.htm (229 words)

	Poisson Process
		The Poisson distribution may not be very helpful in solving this question.
		Observe that we are not given the mean (a data needed for calculations involving the Poisson distribution), but are told that there is a constant probability of success (where "success" is defined as a random person believing the rumour).
		i m not able to understand how to sort out as the poisson process involves the meu and t and in the question we have probability so it's quite confusing to mee
	www.physicsforums.com /showthread.php?p=1019227#post1019227 (557 words)

	Poisson Change-point Procedure (Site not responding. Last check: 2007-10-13)
		Statistical methods for the estimation of the change-point in a Poisson process
		Enter the URL of the file containing your data.
		Continuous-time Estimation of a Change-point in a Poisson Process.
	www.stat.sc.edu /rsrch/gasp/poicha (59 words)

	The Poisson Arrival Model (Site not responding. Last check: 2007-10-13)
		A Poisson process is a sequence of events ``randomly spaced in time."
		of a Poisson process is the average number of events per unit time
		To learn more about the mathematics of the Poisson process,
	networks.ecse.rpi.edu /~vastola/pslinks/perf/node30.html (57 words)

	Poisson Process (Site not responding. Last check: 2007-10-13)
		Next: Classification and Regression Trees Up: Discrete Probability Theory Previous: Poisson
		Here we consider the Poisson random variable Y as a function of time, Y(t).
		The process has stationary independent increments if in addition the random variables
	cda.mrs.umn.edu /~anderson/me3/prob/node22.html (93 words)

	Poisson process - Java (via CobWeb/3.1 planetlab2.isi.jhu.edu) (Site not responding. Last check: 2007-10-13)
		Register for FREE and Post your Question Now!
		I need to get some idea about poisson process to make a simulator, does
		anyone know where I can get an example code for poisson process?
	www.thescripts.com.cob-web.org:8888 /forum/thread15821.html (75 words)

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