33 lines
427 B
Markdown
33 lines
427 B
Markdown
# Landau PDF
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## Pathological probability distribution
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Because of its fat tail:
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\begin{align*}
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E[x] &\longrightarrow + \infty \\
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V[x] &\longrightarrow + \infty
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\end{align*}
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No closed form for parameters.
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## Landau median
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The median of a PDF is defined as:
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$$
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Q_L(x) = \frac{1}{2}
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$$
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- CDF computed by numerical integration,
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- QDF computed by numerical root-finding (Brent)
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hence:
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$$
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m_L = 1.3557804...
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$$
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o
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