From 196b21e0bffce0a67bbeb1f92d83852fb423d568 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Gi=C3=B9=20Marcer?= Date: Tue, 9 Jun 2020 14:51:34 +0000 Subject: [PATCH] misc: remove useless staffs from notes-moyal.md --- slides/misc/notes-moyal.md | 26 -------------------------- 1 file changed, 26 deletions(-) diff --git a/slides/misc/notes-moyal.md b/slides/misc/notes-moyal.md index 5bb921d..f8fa9dd 100644 --- a/slides/misc/notes-moyal.md +++ b/slides/misc/notes-moyal.md @@ -1,17 +1,3 @@ -The Moyal distribution, which is a steepest descent approximation of the -Landau distribition, is defines as: -$$ - \exp \left( - \frac{x - \mu }{2 \sigma} - - \frac{1}{2} \exp \left( - \frac{x -\mu}{\sigma} \right) \right) -$$ -Mean $m$ and variance $\sigma$: -$$ - m = \mu + \sigma [ \gamma + \ln(2) ] \et \sigma = \frac{\pi^2 \sigma^2}{2} -$$ -Median: -$$ - \mu - \sigma \left[ 2 \text{erf}^{-1} \left( \frac{1}{2} \right)^2 \right] -$$ skewness and kurtosis are constant: $$ s = \frac{28 \sqrt{2} Z(3)]{\pi^3} \et k = 7 @@ -20,15 +6,3 @@ max value: $$ \frac{1}{\sqrt{2 e \pi}} $$ -cdf: -$$ - \text{erf} \left( \frac{\exp \left( - - \frac{x - \mu}{2 \sigma} \right)}{\sqrt{2}} \right) -$$ - -$\mu$ is the location parameter and $\sigma$ is the scale parameter. -The Moyal distribution was first proposed in a 1955 paper by physicist J. E. -Moyal. The distribution models the energy lost by a fast charged particle -(and hence the number of ion pairs produced) during ionization. Historically, -the Moyal distribution has been utilized in the approximation of the Landau -Distribution and has since found use in modeling a wide array of phenomena.