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In probability theory and statistics, the Laplace distribution is a continuous probability distribution named after Pierre-Simon Laplace.It is also sometimes called the double exponential distribution, because it can be thought of as two exponential distributions (with an additional location parameter) spliced together along the abscissa, although the term is also sometimes used to refer to ...
In statistics, the double exponential distribution may refer to Laplace distribution, or bilateral exponential distribution, consisting of two exponential distributions glued together on each side of a threshold; Gumbel distribution, the cumulative distribution function of which is an iterated exponential function (the exponential of an ...
The Gumbel distribution is a particular case of the generalized extreme value distribution (also known as the Fisher–Tippett distribution). It is also known as the log-Weibull distribution and the double exponential distribution (a term that is alternatively sometimes used to refer to the Laplace distribution).
A double exponential function. Double exponential time, a task with time complexity roughly proportional to such a function; 2-EXPTIME, the complexity class of decision problems solvable in double-exponential time by a deterministic Turing machine. Double exponential distribution, which may refer to: Laplace distribution, a bilateral ...
The square of a standard normal random variable has a chi-squared distribution with one degree of freedom. If X is a Student’s t random variable with ν degree of freedom, then X 2 is an F (1,ν) random variable. If X is a double exponential random variable with mean 0 and scale λ, then |X| is an exponential random variable with mean λ.
D: Laplace distribution, also known as the double exponential distribution, red curve (two straight lines in the log-scale plot), excess kurtosis = 3; S: hyperbolic secant distribution, orange curve, excess kurtosis = 2; L: logistic distribution, green curve, excess kurtosis = 1.2
The relationship between the exponential distribution and the Laplace distribution allows for a simple method for simulating bivariate asymmetric Laplace variables (including for the case of =). Simulate a bivariate normal random variable vector Y {\displaystyle \mathbf {Y} } from a distribution with μ 1 = μ 2 = 0 {\displaystyle \mu _{1}=\mu ...
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 ...