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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 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 Weibull distribution interpolates between the exponential distribution with intensity / when = and a Rayleigh distribution of mode = / when =. The Weibull distribution (usually sufficient in reliability engineering ) is a special case of the three parameter exponentiated Weibull distribution where the additional exponent equals 1.
When one or more parameter(s) of a distribution are random variables, the compound distribution is the marginal distribution of the variable. Examples: If X | N is a binomial (N,p) random variable, where parameter N is a random variable with negative-binomial (m, r) distribution, then X is distributed as a negative-binomial (m, r/(p + qr)).
The hypoexponential is a series of k exponential distributions each with their own rate , the rate of the exponential distribution. If we have k independently distributed exponential random variables X i {\displaystyle {\boldsymbol {X}}_{i}} , then the random variable,
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 ...
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.