The Laplace distribution, introduced by Pierre-Simon Laplace, is a continuous probability distribution also known as the double exponential distribution. It describes the difference between two identically distributed variables and is represented by a specific density function. The cumulative density function varies based on the value of x relative to the parameter θ, and the distribution spans the range from negative to positive infinity.

1. Laplace Distribution

2. Laplace Distribution: Definition
 Introduced by Pierre-Simon Laplace
It is a continuous probability distribution
Also known as double exponential distribution or Gumbel distribution
Govern the difference between the two identical distributed variable
Increase of Laplace motion or a variance gamma process calculated over the time
represents Laplace distribution
A variable shows Laplace(μ, b) distribution when the density function is defined as

3. Laplace Distribution
Cumulative Density function is given by
F(x|θ,λ) =( ½) exp (− |x−θ|/ λ ) ,when(x ≤ θ),
And
F(x|θ,λ) = 1− 1/2 exp( − |θ −x| λ ) ,when(x > θ)
Contrary to the exponential, the Laplace is defined between the range
−∞ < x < ∞

4. Laplace Distribution

5. Laplace Distribution

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