Search results
Results from the WOW.Com Content Network
A visual depiction of a Poisson point process starting. In probability theory, statistics and related fields, a Poisson point process (also known as: Poisson random measure, Poisson random point field and Poisson point field) is a type of mathematical object that consists of points randomly located on a mathematical space with the essential feature that the points occur independently of one ...
A Lévy process may thus be viewed as the continuous-time analog of a random walk. The most well known examples of Lévy processes are the Wiener process, often called the Brownian motion process, and the Poisson process. Further important examples include the Gamma process, the Pascal process, and the Meixner process.
() is a compound Poisson process, corresponding to the pure point part; is a square integrable pure jump martingale that almost surely has a countable number of jumps on a finite interval, corresponding to the singular continuous part.
A compound Poisson process is a continuous-time stochastic process with jumps. The jumps arrive randomly according to a Poisson process and the size of the jumps is also random, with a specified probability distribution.
The Poisson random measure with intensity measure is a family of random variables {} defined on some probability space (,,) such that i) ∀ A ∈ A , N A {\displaystyle \forall A\in {\mathcal {A}},\quad N_{A}} is a Poisson random variable with rate μ ( A ) {\displaystyle \mu (A)} .
A Poisson (counting) process on the line can be characterised by two properties : the number of points (or events) in disjoint intervals are independent and have a Poisson distribution. A Poisson point process can also be defined using these two properties. Namely, we say that a point process is a Poisson point process if the following two ...
In queueing theory, a discipline within the mathematical theory of probability, Burke's theorem (sometimes the Burke's output theorem [1]) is a theorem (stated and demonstrated by Paul J. Burke while working at Bell Telephone Laboratories) asserting that, for the M/M/1 queue, M/M/c queue or M/M/∞ queue in the steady state with arrivals is a Poisson process with rate parameter λ:
The shift geometric distribution is discrete compound Poisson distribution since it is a trivial case of negative binomial distribution. This distribution can model batch arrivals (such as in a bulk queue [5] [9]). The discrete compound Poisson distribution is also widely used in actuarial science for modelling the distribution of the total ...