diff --git a/VERSION b/VERSION index b1e80bb..845639e 100644 --- a/VERSION +++ b/VERSION @@ -1 +1 @@ -0.1.3 +0.1.4 diff --git a/probstat.tex b/probstat.tex index e68994f..ded13d4 100644 --- a/probstat.tex +++ b/probstat.tex @@ -286,7 +286,7 @@ % Gamma \newcommandx\gam[1][1={\alpha,\beta}]{\textrm{Gamma}\left({#1}\right)} \newcommandx\dgamma[3][1=x,2=\alpha,3=\beta]% -{\frac{1}{\Gamma\left( #2 \right) #3^{#2}} #1^{#2 -1}e^{- #1 / #3}} +{\frac{#3^{#2}}{\Gamma\left( #2 \right)} #1^{#2-1}e^{-#3#1}} % InverseGamma \newcommandx\invgamma[1][1={\alpha,\beta}]{\textrm{InvGamma}\left({#1}\right)} diff --git a/stat-cookbook.tex b/stat-cookbook.tex index 9545270..d524006 100644 --- a/stat-cookbook.tex +++ b/stat-cookbook.tex @@ -25,6 +25,7 @@ \usepackage{multicol} \usepackage{rotating} \usepackage{tikz} +\usepackage{threeparttable} \usepackage{url} \usepackage{xspace} @@ -185,7 +186,7 @@ \subsection{Discrete Distributions} \subsection{Continuous Distributions} -\begin{center} +\begin{threeparttable} \small %\newcolumntype{L}{>{\varwidth[c]{\linewidth}}l<{\endvarwidth}} \newcolumntype{M}{>{\begin{math}\displaystyle}c<{\end{math}}} @@ -244,14 +245,14 @@ \subsection{Continuous Distributions} & \frac{2d_2^2(d_1+d_2-2)}{d_1(d_2-2)^2(d_2-4)} %\; d_2 > 4 & \\[3ex] - Exponential & \ex & \pex & \dex & + Exponential\tnote{$\ast$} & \ex & \pex & \dex & \beta & \beta^2 & - \frac{1}{1-\beta s} \left(s < 1/\beta \right) \\[3ex] + \frac{1}{1-\frac{s}{\beta}} \left(s<\beta\right) \\[3ex] - Gamma & \gam & - \frac{\gamma(\alpha,x/\beta)}{\Gamma(\alpha)} & \dgamma & - \alpha\beta & \alpha\beta^2 & - \left( \frac{1}{1-\beta s} \right)^\alpha \left( s < 1/\beta \right)\\[3ex] + Gamma\tnote{$\ast$} & \gam & + \frac{\gamma(\alpha,\beta x)}{\Gamma(\alpha)} & \dgamma & + \frac{\alpha}{\beta} & \frac{\alpha}{\beta^2} & + \left(\frac{1}{1-\frac{s}{\beta}} \right)^\alpha \left(s<\beta\right)\\[3ex] Inverse Gamma & \invgamma & \pinvgamma & \dinvgamma & \frac{\beta}{\alpha-1} \; \alpha>1 & @@ -284,7 +285,12 @@ \subsection{Continuous Distributions} \bottomrule \end{tabular} -\end{center} +\begin{tablenotes} +\item[$\ast$] We use the \emph{rate} parameterization where + $\beta=\frac{1}{\lambda}$. Some textbooks use $\beta$ as \emph{scale} + parameter instead~\cite{Wasserman03}. +\end{tablenotes} +\end{threeparttable} \begin{figure}[H] \includegraphics[scale=0.35]{figs/uniform-pdf.pdf}