 Laplace - Maple Help

Statistics[Distributions]

 Laplace
 Laplace distribution Calling Sequence Laplace(a, b) LaplaceDistribution(a, b) Parameters

 a - location parameter b - scale parameter Description

 • The Laplace distribution is a continuous probability distribution with probability density function given by:

$f\left(t\right)=\frac{{ⅇ}^{-\frac{\left|t-a\right|}{b}}}{2b}$

 subject to the following conditions:

$a::\mathrm{real},0

 • The Laplace variate with location parameter 0 and scale parameter b is related to two independent Exponential variates $\mathrm{E1}$ and $\mathrm{E2}$ by Laplace(0,b) ~ E1 - E2.
 • Note that the Laplace command is inert and should be used in combination with the RandomVariable command. Examples

 > $\mathrm{with}\left(\mathrm{Statistics}\right):$
 > $X≔\mathrm{RandomVariable}\left(\mathrm{Laplace}\left(a,b\right)\right):$
 > $\mathrm{PDF}\left(X,u\right)$
 $\frac{{{ⅇ}}^{{-}\frac{\left|{-}{u}{+}{a}\right|}{{b}}}}{{2}{}{b}}$ (1)
 > $\mathrm{PDF}\left(X,0.5\right)$
 $\frac{{0.5000000000}{}{{ⅇ}}^{{-}\frac{{1.}{}\left|{-}{0.5}{+}{a}\right|}{{b}}}}{{b}}$ (2)
 > $\mathrm{Mean}\left(X\right)$
 ${a}$ (3)
 > $\mathrm{Variance}\left(X\right)$
 ${2}{}{{b}}^{{2}}$ (4) References

 Evans, Merran; Hastings, Nicholas; and Peacock, Brian. Statistical Distributions 3rd ed. Hoboken: Wiley, 2000.
 Johnson, Norman L.; Kotz, Samuel; and Balakrishnan, N. Continuous Univariate Distributions. 2nd ed. 2 vols. Hoboken: Wiley, 1995.
 Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.