analistica/slides/sections/2.md

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Landau PDF

Pathological probability distribution

Because of its fat tail:

\begin{align*} E[x] &\longrightarrow + \infty \ V[x] &\longrightarrow + \infty \end{align*}

No closed form for parameters.

Landau median

The median of a PDF is defined as:


  Q_L(x) = \frac{1}{2}
  • CDF computed by numerical integration,
  • QDF computed by numerical root-finding (Brent)

hence:


  m_L = 1.3557804...

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