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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 ...
A chi-squared distribution with 2 degrees of freedom (k = 2) is an exponential distribution with a mean value of 2 (rate λ = 1/2 .) A Weibull distribution with shape parameter k = 1 and rate parameter β is an exponential distribution with rate parameter β.
The shifted Gompertz distribution; The type-2 Gumbel distribution; The Weibull distribution or Rosin Rammler distribution, of which the exponential distribution is a special case, is used to model the lifetime of technical devices and is used to describe the particle size distribution of particles generated by grinding, milling and crushing ...
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 ...
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 distribution of the product of a random variable having a uniform distribution on (0,1) with a random variable having a gamma distribution with shape parameter equal to 2, is an exponential distribution. [18]
The Erlang distribution is the distribution of a sum of independent exponential variables with mean / each. Equivalently, it is the distribution of the time until the kth event of a Poisson process with a rate of . The Erlang and Poisson distributions are complementary, in that while the Poisson distribution counts the events that occur in a ...
The exponential distribution, for which the density function is (|) = {, <, is the maximum entropy distribution among all continuous distributions supported in [0,∞) that have a specified mean of 1/λ.