1.5 KiB
1.5 KiB
Goal
Goal
- Generate a sample
Lof points from a Landau PDF - Generate a sample
Mof points from a Moyal PDF
. . .
- Implement a bunch of statistical tests
. . .
- Check if they work:
- the sample
Ltruly comes from a Landau PDF - the sample
Mdoes not come from a Landau PDF
- the sample
Why?
The Landau and Moyal PDFs are really similar. Historically, the latter was utilized in the approximation of the former.
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Two similar distributions
:::: {.columns} ::: {.column width=50%} Landau PDF
$$
L(x) = \frac{1}{\pi} \int \limits_{0}^{+ \infty}
dt \, e^{-t \ln(t) -xt} \sin (\pi t)
:::
::: {.column width=50%} Moyal PDF
$$
M(x) = \frac{1}{\sqrt{2 \pi}} \exp \left[ - \frac{1}{2}
\left( x + e^{- x} \right) \right]
::: ::::
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Two similar distributions
Statistical tests
. . .
- Parameters comparison:
- compatibility between expected and observed PDF parameters
. . .
- Kolmogorov - Smirnov:
- compatibility between expected and observed CDF
. . .
- Trapani test:
- compatibiity between expected and observed mean