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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.
Exponential (disambiguation) Exponential backoff; Exponential decay; Exponential dichotomy; Exponential discounting; Exponential diophantine equation; Exponential dispersion model; Exponential distribution; Exponential error; Exponential factorial; Exponential family; Exponential field; Exponential formula; Exponential function; Exponential ...
For example, suppose that X is a random variable, the lifetime of a car engine, expressed in terms of "number of miles driven until the engine breaks down". It is clear, based on our intuition, that an engine which has already been driven for 300,000 miles will have a much lower X than would a second (equivalent) engine which has only been ...
The reciprocal 1/X of a random variable X, is a member of the same family of distribution as X, in the following cases: Cauchy distribution, F distribution, log logistic distribution. Examples: If X is a Cauchy ( μ , σ ) random variable, then 1/ X is a Cauchy ( μ / C , σ / C ) random variable where C = μ 2 + σ 2 .
In some contexts the probability distribution is described, not by the cumulative distribution function, by the cumulative frequency of a property X, defined as the number of elements per meter (or area unit, second etc.) for which X > x applies, where x is a variable real number. As an example, [citation needed] the cumulative distribution of ...
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 ...
In probability theory, the matrix-exponential distribution is an absolutely continuous distribution with rational Laplace–Stieltjes transform. [1] They were first introduced by David Cox in 1955 as distributions with rational Laplace–Stieltjes transforms .
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