PropertiesTableLaplace.tex

% !TEX encoding = UTF-8 Unicode 
% !TEX root = FieldGuide.tex

\begin{table*}[t!]
\caption[Laplace distribution -- Properties]{Properties of the Laplace distribution}
\begin{align*}
\text{\hyperref[PropertiesSec]{Properties}}  \quad& \\
\text{notation}\quad & \op{Laplace}(x\given \pLoc, \theta) 				\checked
\\ 
\text{PDF} \quad & \frac{1}{2 |\theta|} e^{- \Left|\frac{x-\pLoc}{\theta}\Right|} 	\checked
\\
\text{CDF} \quad & 
\begin{cases}
\phantom{\tfrac{1}{2} -\ } \frac{1}{2} e^{ - \Left|\frac{x-\pLoc}{\theta}\Right| } & x\leq \pLoc  \checked
\\
1 - \tfrac{1}{2} e^{ - \Left|\frac{x-\pLoc}{\theta}\Right| } & x\geq \pLoc 			\checked
\end{cases}
\\
\text{parameters}\quad & \pLoc,\ \theta \text{ in } \mathbb{R}				\checked
\\
\text{support} \quad & x \in [ -\infty, +\infty] 							\checked
\\
\text{median} \quad & \pLoc                            							\checked
\\
\text{mode} \quad & \pLoc 										\checked
\\
\text{mean} \quad & \pLoc  										\checked
\\
\text{variance} \quad & 2\theta^2 									\checked
\\
\text{skew} \quad & 0 											\checked
\\ 
\text{ex. kurtosis} \quad & 3 											\checked
\\ 
\text{entropy} \quad & 1+ \ln( 2 |\theta|) 								\checked
\\ 
\text{MGF} \quad &  \frac{\exp(\pLoc t) }{1- \theta^2 t^2}					\checked
\\
\text{CF} \quad & \frac{\exp(i\pLoc t) }{1+ \theta^2 t^2}					\checked
\end{align*}
\end{table*}