What is the Laplace distribution?

The Laplace distribution is a probability distribution that models the difference between two independent exponential random variables.

The Laplace distribution, also known as the double exponential distribution, is a continuous probability distribution that is symmetric around its mean. It is often used in statistics to model the difference between two independent exponential random variables. The probability density function (PDF) of the Laplace distribution is given by:

f(x; μ, b) = 1/(2b) * exp(-|x-μ|/b)

where μ is the location parameter and b is the scale parameter. The mean and variance of the Laplace distribution are both equal to μ. The Laplace distribution has heavy tails, which means that it has a higher probability of producing extreme values than a normal distribution.

The Laplace distribution is often used in image processing and computer vision, where it is used to model the noise in images. It is also used in finance to model the distribution of stock returns, as it can capture the fat tails and skewness that are often observed in financial data.

In summary, the Laplace distribution is a probability distribution that is often used to model the difference between two independent exponential random variables. It is symmetric around its mean, has heavy tails, and is used in a variety of fields including statistics, image processing, and finance.