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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 known as the double exponential distribution, because it can be thought of as two exponential distributions (with an additional location parameter) spliced together back-to-back. The difference between two independent identically distributed exponential random variables is governed by a Laplace distribution.
Distribution, density, and quantile function
The pdf of the Laplace distribution is also reminiscent of the normal distribution; however, whereas the normal distribution is expressed in terms of the squared difference from the mean μ, the Laplace density is expressed in terms of the absolute difference from the mean. Consequently the Laplace distribution has fatter tails than the normal distribution.
The inverse cumulative distribution function is given by
A Laplace(0, b) variate can be generated as the difference of two i.i.d. Exponential(1/b) variates. Equivalently, a Laplace(0, 1) variate can be generated as the logarithm of the ratio of two iid uniform variates.
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