Poisson Process model

The drought coeffieient ) for a period is equal to the nuraher of days with precipitation divided by the total number of days. It is used to estimate the probability of a day being dry (dy,) for a given time (t) since rainfall in the integrated Poisson Process model d>j = 1 ... 

Goldman, N., Maximum likelihood inference of phylogenetic trees, with special reference to a Poisson process model of DNA substitution and to parsimony analyses, Syst. Zool., 39, 345-361, 1990. 

Goel s generalized nonhomogeneous Poisson process model (1983)... 

Based on a Poisson process model of earthquake occurrences and an assumption that damaged buildings are immediately retrofitted to their original intact conditions... 

The Crow AMSSA is a statistical model which uses the Weibull failure rate function to describe the relationship between accumulated time to failure and test time, being a Non-Homogeneous Poisson Process Model. This approach is applied in order to demonstrate the effect of corrective and preventive actions on reliability when a product is being developed or for repairable systems during operation phase (Crow, 2012). Thus, whenever improvement is implemented during test (Test-Fix-Test) or maintenance, the Crow AMSAA model is appropriated to predict reliability growth and expected cumulative number of failures. The expected cumulative number of failures is mathematically represented by the following equation ... 

The PLP is a well-known NHPP model used to study the reliability of the repairable systems. Duane (1964) was the first to report that the cumulative number of failures of such systems up to time t, N, often have a power-law growth pattern. Then, Crow (1974) formulated the corresponding model as a nonhomogeneous Poisson process model. The reliability function at time t are defined by the following equation ... 

Another type of Bayesian model that is useful for paieoseismoiogy is an age-depth model for sedimentary sequences. Such models can be used when there are a series of radiocarbon dates in a single sediment column, with depth information. Most commonly, these are used for cores, but could also be applied to other types of section if a single depth scale can be defined. Like other Bayesian models, there needs to be a mathematical model for the deposition process. One such model is the Poisson process model implemented in OxCal. In this model, the assumption is that the deposition is random which allows for flexibility in an otherwise... 

Radiocarbon Dating in Paleoseismology, Fig. 6 Lake and marine cores provide a useful source of evidence for past seismic events. Where radiocarbon is used to date such cores, age-depth models can be used to integrate the information from the dated samples and the depths of the samples and events of Interest. The central panel shows schematically the underlying assumption for a simple Poisson process model, where randomly varying... 

Nature In monitoring a moving threadhne, one criterion of quality would be the frequency of broken filaments. These can be identified as they occur through the threadhne by a broken-filament detector mounted adjacent to the threadhne. In this context, the random occurrences of broken filaments can be modeled by the Poisson distribution. This is called a Poisson process and corresponds to a probabilistic description of the frequency of defects or, in general, what are called arrivals at points on a continuous line or in time. Other examples include ... 

Poisson process is often a reasonable model for the arrival times of... 

The Monte Carlo method as described so far is useful to evaluate equilibrium properties but says nothing about the time evolution of the system. However, it is in some cases possible to construct a Monte Carlo algorithm that allows the simulated system to evolve like a physical system. This is the case when the dynamics can be described as thermally activated processes, such as adsorption, desorption, and diffusion. Since these processes are particularly well defined in the case of lattice models, these are particularly well suited for this approach. The foundations of dynamical Monte Carlo (DMC) or kinetic Monte Carlo (KMC) simulations have been discussed by Eichthom and Weinberg (1991) in terms of the theory of Poisson processes. The main idea is that the rate of each process that may eventually occur on the surface can be described by an equation of the Arrhenius type ... 

Nonsolvent bath, polymer precipitation by immersion in, 15 808-811 Nonspecific elution, in affinity chromatography, 6 398, 399 Nonstationary Poisson process, in reliability modeling, 26 989 Non-steady-state conduction, 9 105 Nonsteroidal antiinflamatory agents/drugs (NSAIDs) 21 231 for Alzheimer s disease, 2 820 for cancer prevention, 2 826 Nonsulfide collectors, 16 649 Nonsulfide flotation, 16 649-650 Nonsulfide mineral flotation collectors used in, 16 648-649t modifiers used in, 16 650, 651t Nonsulfide ores, 16 598, 624... 

The exponential distribution with parameter X is the distribution of waiting times ( distance in time) between events which take place at a mean rate of X. It is also the distribution of distances between features which have a uniform probability of occurrence (Poisson process), such as the simplest model of faults on a map. The gamma distribution with parameter n and X l, where n is an integer is the distribution of the waiting time between the first and the nth successive events in a Poisson process. Alternatively, the distribution /(t), such as... 

Due to system complexity and paucity of information about the reaction mechanism(s), a Markov process model is proposed with probability pk = a cxpf -X)/k of the production of k ions of the anionic species X is the mean of the postulated Poisson distribution. The model also stipulates a probability q of reaction of the anionic species during two successive equal time periods of At each. 

We can model this as a Poisson process and use the simple formula ... 

Halliday R, Gregory K, Naylor H, et al Beyond drug effects and dependent variables the use of the Poisson-Erlang model to assess the effects of d-amphetamine on information processing. Acta Psychologica 73 35-54, 1990 Hallman M, Bry K, Hoppu K, et al Inositol supplementation in premature infants with respiratory distress syndrome. N Engl J Med 326 1233-1239, 1992 Hamik A, Peroutka S MCPP interaction with neurotransmitter receptors in human brain. Biol Psychiatry 25 569-575, 1989... 

One hypothetical model for the deposition is the purely random Poisson process (Wei, 1984) where any surface is equally likely to be the next deposition site, regardless of whether it is bare alumina or covered by previous depositions. For such a model, the probability of a surface covered with n number of deposits would be... 

With sufficiently complex samples, particularly biological and environmental samples, the frequency of overlap can be estimated by statistical means. In a statistical model developed by Davis and this author [33], far-reaching conclusions follow from a simple basic assumption the probability that any small interval dx along the separation path x is occupied by a component peak center is A dx, where A is a constant. This assumption defines a Poisson process and leads to well-known statistical conclusions. 

The results of this review show that the emergence of a non-Poisson distribution of light on and light off states cannot be derived from the modulation of a Poisson model, which, without modulation, would account for the experimental results of Dehmelt [140]. This issue is still unsettled. However, it seems to be evident that the model must be of the renewal type, as proved by Brokmann et al. [98]. More recently, other results have been found [99] confirming with surprising accuracy the renewal character of these non-Poisson processes. 

Equation (5) is an example of the Poisson process in probability theory [9]. S decays slowly with t, so that enough sites survive even at long times to continue forming new coke. This simple model lends itself naturally to the distinction of coke depositing on clean sites, monolayer coke concentration C , and coke depositing on already-coked sites, multilayer coke concentration Cm- That is, C (/) = CJf) + CM t) at all times. A simple site balance yields... 

The linear chromatographic process is modeled as a composite Poisson process a chain of exponentially distributed fly times, followed by exponentially distributed adsorption times are generated. When adsorbed, the molecule is stationary the mean adsorption time is t . When desorbed, the molecule travels with the velocity of the mobile phase the mean fly time—residence time between a desorption and the subsequent adsorption—in the mobile phase is t. The elution time of the molecule is recorded when it reaches the end of the colxunn after n adsorption-desorption events on the average. The distribution of the single molecule elution times gives the band profile. 

One of the simplest models of queuing is the following one. Let customers arrive at a service point in a Poisson process [see 2.2-3] of rate X [customers arriving per unit time]. Suppose that customers can be served only one at a time and that customers arriving to find the server busy queue up in the order of arrival until their turn for service comes. Such a queuing policy is called First In First Out (FIFO). Further, suppose that the length of time taken to serve a customer is a random variable with the exponential p.d.f. = (probability density function) given by... 

In the following, we derive the Kolmogorov differential equation on the basis of a simple model and report its various versions. In principle, this equation gives the rate at which a certain state is occupied by the system at a certain time. This equation is of a fundamental importance to obtain models discrete in space and continuous in time. The models, later discussed, are the Poisson Process, the Pure Birth Process, the Polya Process, the Simple Death Process and the Birth-and-Death Process. In section 2.1-3 this equation, i.e. Eq.2-30, has been derived for Markov chains discrete in space and time. 

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