From: W. Trevor King Date: Mon, 20 May 2013 13:22:31 +0000 (-0400) Subject: sawsim/discussion.tex: Add Gumbel \mu to the nomenclature X-Git-Tag: v1.0~159 X-Git-Url: http://git.tremily.us/?a=commitdiff_plain;h=3561d3ad392cf1f6b7defbd1987d7f5573ceaeeb;p=thesis.git sawsim/discussion.tex: Add Gumbel \mu to the nomenclature Thanks Mom! --- diff --git a/src/sawsim/discussion.tex b/src/sawsim/discussion.tex index c0a3e37..713f1fc 100644 --- a/src/sawsim/discussion.tex +++ b/src/sawsim/discussion.tex @@ -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}