sawsim/discussion.tex: Add Gumbel \mu to the nomenclature
authorW. Trevor King <wking@tremily.us>
Mon, 20 May 2013 13:22:31 +0000 (09:22 -0400)
committerW. Trevor King <wking@tremily.us>
Mon, 20 May 2013 13:22:31 +0000 (09:22 -0400)
Thanks Mom!

src/sawsim/discussion.tex

index c0a3e37cc8ce878ff150741525f905637d97155b..713f1fc144ba1e8f9760cd2d54cbb1e21a2eb703 100644 (file)
@@ -765,12 +765,14 @@ the mean of the Gumbel probability density
 \begin{equation}
   P(x) = \frac{1}{\beta} \exp\p[{\frac{x-\alpha}{\beta}
                                  -\exp\p({\frac{x-\alpha}{\beta}})
-                                 }]
+                                 }]  \label{eq:sawsim:gumbel-x}
 \end{equation}
 is given by $\mu=\alpha-\gamma\beta$, and the variance is
 $\sigma^2=\frac{1}{6}\pi^2\beta^2$, where $\gamma=0.57721566\ldots$ is
 the Euler-Mascheroni constant.  Selecting $\beta=1/a=k_BT/\dd x$,
 $\alpha=-\beta\ln(\kappa\beta/kv)$, and $F=x$ we have
+\nomenclature{$\mu$}{The mean of a distribution (e.g. the Gumbel
+  distribution, \cref{eq:sawsim:gumbel-x}).}
 \begin{align}
   P(F)
     &= \frac{1}{\beta} \exp\p[{\frac{F+\beta\ln(\kappa\beta/kv)}{\beta}