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...process]] that is a generalization of a [[Poisson process]]. Mixed Poisson processes are simple example for [[Cox process]]es. ...</math> iff <math> \xi </math> conditionally on <math> X=x </math> is a [[Poisson process]] on <math> S </math> with [[intensity measure]] <math> x\mu </math ...

...and can, for example, be used to simulate these more complex Poisson point processes in a similar manner to [[inverse transform sampling]]. ...re]] <math> \mu </math>, then <math> \xi \circ f^{-1} </math> is a Poisson point process on <math> Y </math> with intensity measure <math> \nu:= \mu \circ f ...

...es Construction of dependent Dirichlet processes based on compound Poisson processes], Neural Information Processing Systems (NIPS), 2010. </ref> The concept is ...ir labeling. This assumption is invalid for modelling temporal and spatial processes in which the order of data points plays a critical role in creating meaning ...

...expresses that a large number of [[renewal process]]es, not necessarily [[Poisson process|Poissonian]], when combined ("superimposed") will have Poissonian p |title = Stochastic Models in Operations Research: Stochastic Processes and Operating Characteristics ...

...y naturally arise from restrictions of ([[mixed Poisson process|mixed]]) [[Poisson process]]es bounded intervals. ...dent]] and let <math> \delta_x </math> denote the [[Dirac measure]] on the point <math> x </math>. ...

...ribution]] on compact sets; for each point <math>\xi</math> of the Poisson point process we pick a set <math>C_\xi</math> from the distribution, and then de | title = Probability Approximations via the Poisson Clumping Heuristic ...

...oint process]] in [[probability theory]]. In simple point processes, every point is assigned the weight one. ...s [[random measure]] on <math> (S, \mathcal S) </math>, is called a simple point process if it can be written as ...

...the distance from that point to its nearest neighbouring point in the same point process. ...P. Waagepetersen. ''Statistical inference and simulation for spatial point processes''. CRC Press, 2003.</ref> which are applied in various [[scientific]] and [ ...

{{Short description|Function that transforms a point process}} ...s operations and the resulting point processes are used in the theory of [[point process]]es and related fields such as [[stochastic geometry]] and [[spatia ...

...8">D. J. Daley and D. Vere-Jones. ''An introduction to the theory of point processes. Vol. {II''}. Probability and its Applications (New York). Springer, New Yo ...NoW Publishers, 2009.</ref> In other words, if the number of points of a point process located in some region of space is a random variable, then the firs ...

...us of a sphere when it first encounters or makes contact with a point of a point process. ...P. Waagepetersen. ''Statistical inference and simulation for spatial point processes''. CRC Press, 2003. [https://dx.doi.org/10.1201/9780203496930]</ref> which ...

...is a [[probability distribution]] that has a larger [[variance]] than a [[Poisson distribution]] with the same [[mean]].<ref>{{Cite journal | last1 = Zou | f The [[Poisson distribution]] is a result of a process where the time (or an equivalent me ...

...ocess, with the type of relocation being dependent on the position of each point. ...ure]] on the point <math> x </math> and let <math> \mu </math> be a simple point measure on <math> S </math>. This means that ...

...er is the Palm expectation of the former, conditioning on the event that a point occurs at the time of the observation. This paradox occurs because large i ...TA). That means that, if the event being conditioned on is a point in a [[Poisson process]] (independent of the process being observed), then the distinction ...

...completely random fashion. It is synonymous with a ''homogeneous [[spatial Poisson process]]''.<ref name="Omaimon2010DataM">O. Maimon, L. Rokach, ''Data Minin ...most other statistical contexts it is referred to the concept of a spatial Poisson process.<ref name="Omaimon2010DataM"/> ...

...l case of a [[continuous-time Markov process]] and a generalisation of a [[Poisson process]]. It defines a continuous process which takes values in the [[natu ...nitions for communicating classes, irreducibility and so on apply to birth processes. By the conditions for recurrence and transience of a [[birth–death process ...

...3">D. J. Daley and D. Vere-Jones. ''An introduction to the theory of point processes. Vol. I''. Probability and its Applications (New York). Springer, New York, ...ss of point processes, which means they can be used to uniquely identify a point process. ...

== Pooled QMLE for Poisson models== ...nal requirements are less stringent, especially compared to [[fixed-effect Poisson model]]s, but the trade off is the possibly strong assumption of no [[unobs ...

...1988.<ref>Lam, Y. (1988). [https://dx.doi.org/10.1007/BF02007241 Geometric processes and replacement problem]. ''Acta Mathematicae Applicatae Sinica''. 4, 366–3 ...tps://dx.doi.org/10.1002/nav.20099 Properties of the geometric and related processes]. ''Naval Research Logistics'' (NRL), 52(7), 607–616.</ref> Given a sequenc ...

...ime are referred to as recurrent event processes, which are different from processes analyzed in time-to-event analysis: whereas time-to-event analysis focuses * Understanding and describing individual event processes ...