Laplace distribution Probabilities
Calculator of Laplace distribution : probabilities, density function (PDF) and cumulative density function (CDF).
Laplace Distribution formulas
X : a random variable following a Laplace distribution
`mu` : location parameter
s : scale parameter (s > 0)
Probability Density Function (PDF)
`f(x) = 1/(2*s)*exp(-|x-mu|/s)`
Cumulative distribution function (CDF)
`F(x) = \int_-oo^x f(t)\ dt`
`F(x) = 1/2*exp((x-mu)/s)` if `x <= mu`
`F(x) = 1-1/2*exp(-(x-mu)/s)` if `x >= mu`
Probabilities
Probability that X is greater than a :
`P(X > a) = 1 - F(a)`
Probability that X is less than b :
`P(X < b) = F(b)`
Probability that X lies between a and b :
`P(a < X < b) = F(b) - F(a)`
See also
Inverse Laplace distribution
Laplace distribution Chart
Statistics Calculators