# Category: Point processes

Determinantal point process
In mathematics, a determinantal point process is a stochastic point process, the probability distribution of which is characterized as a determinant of some function. Such processes arise as important
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
Point Processes
Point Processes is a book on the mathematics of point processes, randomly located sets of points on the real line or in other geometric spaces. It was written by David Cox and Valerie Isham, and publi
Hawkes process
In probability theory and statistics, a Hawkes process, named after Alan G. Hawkes, is a kind of self-exciting point process. It has arrivals at times where the infinitesimal probability of an arrival
Laplace functional
In probability theory, a Laplace functional refers to one of two possible mathematical functions of functions or, more precisely, functionals that serve as mathematical tools for studying either point
Binomial process
A binomial process is a special point process in probability theory.
Factorial moment measure
In probability and statistics, a factorial moment measure is a mathematical quantity, function or, more precisely, measure that is defined in relation to mathematical objects known as point processes,
Index of dispersion
In probability theory and statistics, the index of dispersion, dispersion index, coefficient of dispersion, relative variance, or variance-to-mean ratio (VMR), like the coefficient of variation, is a
Dynamic contagion process
In applied probability, a dynamic contagion process is a point process with stochastic intensity that generalises the Hawkes process and Cox process with exponentially decaying shot noise intensity.
Overdispersion
In statistics, overdispersion is the presence of greater variability (statistical dispersion) in a data set than would be expected based on a given statistical model. A common task in applied statisti
Palm–Khintchine theorem
In probability theory, the Palm–Khintchine theorem, the work of Conny Palm and Aleksandr Khinchin, expresses that a large number of renewal processes, not necessarily Poissonian, when combined ("super
Generalized renewal process
In the mathematical theory of probability, a generalized renewal process (GRP) or G-renewal process is a stochastic point process used to model failure/repair behavior of repairable systems in reliabi
Point process
In statistics and probability theory, a point process or point field is a collection of mathematical points randomly located on a mathematical space such as the real line or Euclidean space.Point proc
Residual time
In the theory of renewal processes, a part of the mathematical theory of probability, the residual time or the forward recurrence time is the time between any given time and the next epoch of the rene
Simple point process
A simple point process is a special type of point process in probability theory. In simple point processes, every point is assigned the weight one.
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
Nu-transform
In the theory of stochastic processes, a ν-transform is an operation that transforms a measure or a point process into a different point process. Intuitively the ν-transform randomly relocates the poi
Point process operation
In probability and statistics, a point process operation or point process transformation is a type of mathematical operation performed on a random object known as a point process, which are often used
Moment measure
In probability and statistics, a moment measure is a mathematical quantity, function or, more precisely, measure that is defined in relation to mathematical objects known as point processes, which are
Renewal theory
Renewal theory is the branch of probability theory that generalizes the Poisson process for arbitrary holding times. Instead of exponentially distributed holding times, a renewal process may have any
Mixed binomial process
A mixed binomial process is a special point process in probability theory. They naturally arise from restrictions of (mixed) Poisson processes bounded intervals.
Kernel (statistics)
The term kernel is used in statistical analysis to refer to a window function. The term "kernel" has several distinct meanings in different branches of statistics.
Complete spatial randomness
Complete spatial randomness (CSR) describes a point process whereby point events occur within a given study area in a completely random fashion. It is synonymous with a homogeneous spatial Poisson pro