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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.
A distribution in an exponential family with parameter θ can be written with probability density function (PDF) = ( () ), where () and () are known functions. A distribution in a natural exponential family with parameter θ can thus be written with PDF = ( ). [Note that slightly different notation is used by the originator of the NEF ...
In probability theory, an exponentially modified Gaussian distribution (EMG, also known as exGaussian distribution) describes the sum of independent normal and exponential random variables. An exGaussian random variable Z may be expressed as Z = X + Y , where X and Y are independent, X is Gaussian with mean μ and variance σ 2 , and Y is ...
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The Template:Infobox probability distribution generates a right-hand side infobox, based on the specified parameters. To use this template, copy the following code in ...
Its complementary cumulative distribution function is a stretched exponential function. The Weibull distribution is related to a number of other probability distributions; in particular, it interpolates between the exponential distribution ( k = 1) and the Rayleigh distribution ( k = 2 and λ = 2 σ {\displaystyle \lambda ={\sqrt {2}}\sigma } ).
The q-deformed exponential and logarithmic functions were first introduced in Tsallis statistics in 1994. [1] However, the q -logarithm is the Box–Cox transformation for q = 1 − λ {\displaystyle q=1-\lambda } , proposed by George Box and David Cox in 1964.