Laplace Distribution Calculator

Compute the probability density, cumulative probability, upper tail, mean, and variance of the Laplace (double exponential) distribution from location and scale.

Input

Enter the location μ and scale b to compute the Laplace distribution probability density, cumulative probability, upper tail, mean, and variance.

Evaluation point x

The point at which to evaluate. Any real number is allowed.

Location μ

The center of the distribution. Any real number is allowed.

Scale b

The parameter that controls the spread. Must be a positive number.

Result

Probability of being at or below x = 1 (lower tail)

0.81606028

Upper tail

0.18393972

Density f(x)

0.18393972

Mean

Variance

Probability density function PDF

Cumulative distribution function CDF

How it works

The Laplace probability density is f(x) = (1 / 2b) e^(−|x−μ| / b). Here μ is the center (location) of the distribution and b is the positive scale parameter that controls the spread.
The cumulative distribution (lower tail) is piecewise: for x below μ, F(x) = (1/2) e^((x−μ)/b); for x at or above μ, F(x) = 1 − (1/2) e^(−(x−μ)/b).
The upper tail probability is 1 − F(x), the chance of being at or above x. Because the distribution is symmetric about μ, both the lower and upper probabilities equal 0.5 at x = μ.
The mean is μ and the variance is 2b². Compared with the normal distribution, the Laplace distribution has heavier tails and a sharper peak.

Reviews

Tell us what you think of this calculator.