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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.
In the four survival function graphs shown above, the shape of the survival function is defined by a particular probability distribution: survival function 1 is defined by an exponential distribution, 2 is defined by a Weibull distribution, 3 is defined by a log-logistic distribution, and 4 is defined by another Weibull distribution.
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]
Cumulative distribution function for the exponential distribution Cumulative distribution function for the normal distribution. In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable, or just distribution function of , evaluated at , is the probability that will take a value less than or equal to .
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 ...
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 = [5]).
Exponential functions with bases 2 and 1/2. In mathematics, the exponential function is the unique real function which maps zero to one and has a derivative equal to its value. . The exponential of a variable is denoted or , with the two notations used interchangeab