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slides: add plot in the Moyal PDF slide

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Michele Guerini Rocco 2020-06-12 16:05:41 +02:00
parent 59d847544e
commit 75a97810e2
1 changed files with 14 additions and 6 deletions
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20
slides/sections/3.md
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@ -1,9 +1,12 @@
# Moyal distribution # Moyal distribution
## Moyal PDF ## Moyal PDF {.b}
:::: {.columns align=center}
::: {.column width=50%}
Standard form: Standard form:
$$ $$
M(z) = \frac{1}{\sqrt{2 \pi}} \exp M(z) = \frac{1}{\sqrt{2 \pi}} \exp
@ -18,13 +21,18 @@ More generally:
- scale parameter $\sigma$ - scale parameter $\sigma$
$$ $$
z = \frac{x - \mu}{\sigma}
\thus
M_{\mu \sigma}(x) = \frac{1}{\sqrt{2 \pi} \sigma} \exp M_{\mu \sigma}(x) = \frac{1}{\sqrt{2 \pi} \sigma} \exp
\left[ - \frac{1}{2} \left( \left[ - \frac{1}{2} \left(
\frac{x - \mu}{\sigma} \frac{x - \mu}{\sigma}
+ e^{-\frac{x - \mu}{\sigma}} \right) \right] + e^{-\frac{x - \mu}{\sigma}} \right) \right]
$$ $$
:::
::: {.column width=50%}
![](images/moyal-pdf.pdf)
:::
::::
## Moyal CDF ## Moyal CDF