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Gaussian process. In probability theory and statistics, a Gaussian process is a stochastic process (a collection of random variables indexed by time or space), such that every finite collection of those random variables has a multivariate normal distribution. The distribution of a Gaussian process is the joint distribution of all those ...
A Poisson point process is characterized via the Poisson distribution. The Poisson distribution is the probability distribution of a random variable (called a Poisson random variable) such that the probability that equals is given by: where denotes factorial and the parameter determines the shape of the distribution.
A stochastic or random process can be defined as a collection of random variables that is indexed by some mathematical set, meaning that each random variable of the stochastic process is uniquely associated with an element in the set. [4][5] The set used to index the random variables is called the index set.
Given a measurable set S, a base probability distribution H and a positive real number , the Dirichlet process is a stochastic process whose sample path (or realization, i.e. an infinite sequence of random variates drawn from the process) is a probability distribution over S, such that the following holds.
Probability theory. A Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happens next depends only on the state of affairs now."
In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate; the distance parameter could be any meaningful mono-dimensional measure of the process, such as time ...
Process capability. The process capability is a measurable property of a process to the specification, expressed as a process capability index (e.g., C pk or C pm) or as a process performance index (e.g., P pk or P pm). The output of this measurement is often illustrated by a histogram and calculations that predict how many parts will be ...
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 independent and identically distributed (IID) holding times that have finite mean. A renewal-reward process additionally has a random sequence of ...