If location or scale are not specified, they assume the default
values of 0 and 1 respectively.
The Laplace distribution with location \(\mu\) and scale \(\phi\) has density
$$
f(x) =
\frac{1}{\sqrt{2}\phi} \exp(-\sqrt{2}|x-\mu|/\phi),$$
where \(-\infty < y < \infty\), \(-\infty < \mu < \infty\) and \(\phi > 0\).
The mean is \(\mu\) and the variance is \(\phi^2\).
The cumulative distribution function, assumes the form
$$
F(x) =
\left\{\begin{array}{ll}
\frac{1}{2} \exp(\sqrt{2}(x - \mu)/\phi) & x < \mu, \\
1 - \frac{1}{2} \exp(-\sqrt{2}(x - \mu)/\phi) & x \geq \mu.
\end{array}\right.$$
The quantile function, is given by
$$
F^{-1}(p) = \left\{\begin{array}{ll}
\mu + \frac{\phi}{\sqrt{2}} \log(2p) & p < 0.5, \\
\mu - \frac{\phi}{\sqrt{2}} \log(2(1-p)) & p \geq 0.5.
\end{array}\right.$$