1.5 KiB
Goal
Goal
Construct six statistical tests to assert whether a sample comes from a Landau distribution
. . .
- Generate a sample
Lfrom a Landau PDF - Generate a sample
Mfrom a Moyal PDF
. . .
H_0: sample following Landau PDF
- can we accept
H_0forL? - can we reject
H_0forM?
Why Moyal?
The Landau and Moyal PDFs are really similar. Historically, the latter was utilized as an approximation of the former.
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Two similar distributions
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$$
L(x) = \frac{1}{\pi} \int \limits_{0}^{+ \infty}
dt \, e^{-t \ln(t) -xt} \sin (\pi t)
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::: {.column width=50%} Moyal PDF
$$
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
. . .
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Properties test:
compatibility between expected and observed PDF properties
. . .
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Kolmogorov - Smirnov test:
compatibility between expected and empirical CDF
. . .
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Trapani test:
test for finite or infinite moments