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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.
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 ...
They showed that the exponentiated Weibull distribution has increasing, decreasing, bathtub, and unimodal hazard rates. The exponentiated exponential distribution proposed by Gupta and Kundu (1999, 2001) is a special case of the exponentiated Weibull family. Later, the moments of the EW distribution were derived by Choudhury (2005).
Beta distribution, for a single probability (real number between 0 and 1); conjugate to the Bernoulli distribution and binomial distribution; Gamma distribution, for a non-negative scaling parameter; conjugate to the rate parameter of a Poisson distribution or exponential distribution, the precision (inverse variance) of a normal distribution, etc.
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 ...
[1] [2] [3] Exponential dispersion models play an important role in statistical theory, in particular in generalized linear models because they have a special structure which enables deductions to be made about appropriate statistical inference.
The probability density function of the wrapped exponential distribution is [1] (;) = = (+) =,for < where > is the rate parameter of the unwrapped distribution. This is identical to the truncated distribution obtained by restricting observed values X from the exponential distribution with rate parameter λ to the range <.
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