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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 ...
The Dagum distribution; The exponential distribution, which describes the time between consecutive rare random events in a process with no memory. The exponential-logarithmic distribution; The F-distribution, which is the distribution of the ratio of two (normalized) chi-squared-distributed random variables, used in the analysis of variance.
The terms "distribution" and "family" are often used loosely: Specifically, an exponential family is a set of distributions, where the specific distribution varies with the parameter; [a] however, a parametric family of distributions is often referred to as "a distribution" (like "the normal distribution", meaning "the family of normal distributions"), and the set of all exponential families ...
The normal distribution is perhaps the most important case. Because the normal distribution is a location-scale family, its quantile function for arbitrary parameters can be derived from a simple transformation of the quantile function of the standard normal distribution, known as the probit function. Unfortunately, this function has no closed ...
The only continuous random variable that is memoryless is the exponential random variable. It models random processes like time between consecutive events. [ 8 ] The memorylessness property asserts that the amount of time since the previous event has no effect on the future time until the next event occurs.
The Erlang distribution is a series of k exponential distributions all with rate . The hypoexponential is a series of k exponential distributions each with their own rate λ i {\displaystyle \lambda _{i}} , the rate of the i t h {\displaystyle i^{th}} exponential distribution.
A phase-type distribution is a probability distribution constructed by a convolution or mixture of exponential distributions. [1] It results from a system of one or more inter-related Poisson processes occurring in sequence , or phases.
The q-exponential distribution is a probability distribution arising from the maximization of the Tsallis entropy under appropriate constraints, including constraining the domain to be positive. It is one example of a Tsallis distribution .