# Category: Poisson point processes

Mixed Poisson process
In probability theory, a mixed Poisson process is a special point process that is a generalization of a Poisson process. Mixed Poisson processes are simple example for Cox processes.
Shot noise
Shot noise or Poisson noise is a type of noise which can be modeled by a Poisson process. In electronics shot noise originates from the discrete nature of electric charge. Shot noise also occurs in ph
Homogeneous Poisson point process
No description available.
Birth process
In probability theory, a birth process or a pure birth process is a special case of a continuous-time Markov process and a generalisation of a Poisson process. It defines a continuous process which ta
Dobiński's formula
In combinatorial mathematics, Dobiński's formula states that the n-th Bell number Bn (i.e., the number of partitions of a set of size n) equals where denotes Euler's number.The formula is named after
Geometric process
In probability, statistics and related fields, the geometric process is a counting process, introduced by Lam in 1988. It is defined as The geometric process. Given a sequence of non-negative random v
Cox process
In probability theory, a Cox process, also known as a doubly stochastic Poisson process is a point process which is a generalization of a Poisson process where the intensity that varies across the und
Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A ma
Zero-inflated model
In statistics, a zero-inflated model is a statistical model based on a zero-inflated probability distribution, i.e. a distribution that allows for frequent zero-valued observations.
Mapping theorem (point process)
The mapping theorem is a theorem in the theory of point processes, a sub-discipline of probability theory. It describes how a Poisson point process is altered under measurable transformations. This al
Compound Poisson process
A compound Poisson process is a continuous-time (random) stochastic process with jumps. The jumps arrive randomly according to a Poisson process and the size of the jumps is also random, with a specif
Poisson random measure
Let be some measure space with -finite measure . The Poisson random measure with intensity measure is a family of random variables defined on some probability space such that i) is a Poisson random va
Poisson point process
In probability, statistics and related fields, a Poisson point process is a type of random mathematical object that consists of points randomly located on a mathematical space. The Poisson point proce
Exponential distribution
In probability theory and statistics, the exponential distribution is the probability distribution of the time between events in a Poisson point process, i.e., a process in which events occur continuo
Poisson clumping
Poisson clumping, or Poisson bursts, is a phenomenon where random events may appear to occur in clusters, clumps, or bursts.
Proportional hazards model
Proportional hazards models are a class of survival models in statistics. Survival models relate the time that passes, before some event occurs, to one or more covariates that may be associated with t
Super-Poissonian distribution
In mathematics, a super-Poissonian distribution is a probability distribution that has a larger variance than a Poisson distribution with the same mean. Conversely, a sub-Poissonian distribution has a