slides: various fixes
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@ -20,8 +20,8 @@ mainfontoptions:
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mathfont: FiraMath-Regular
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mathfont: FiraMath-Regular
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references:
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references:
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- type: article-journal
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- id: trapani15
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id: trapani15
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type: article-journal
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author:
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author:
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family: Trapani
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family: Trapani
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given: Lorenzo
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given: Lorenzo
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@ -29,15 +29,14 @@ references:
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container-title: Journal of Econometrics
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container-title: Journal of Econometrics
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issued:
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issued:
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year: 2015
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year: 2015
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- type: book
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- id: silver86
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id: silver86
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type: book
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author:
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author:
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family: Silverman
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family: Silverman
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given: Bernard W.
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given: Bernard W.
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title: Density Estimation for Statistics and Data Analysis
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title: Density Estimation for Statistics and Data Analysis
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issued:
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issued:
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year: 1986
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year: 1986
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- id: robertson74
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- id: robertson74
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type: article-journal
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type: article-journal
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author:
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author:
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@ -81,18 +81,18 @@ utilized as an approximation of the former.
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. . .
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. . .
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- **Properties test**:
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- **Properties test**
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compatibility between expected and observed PDF properties
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compatibility between expected and observed PDF properties
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. . .
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. . .
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- **Kolmogorov - Smirnov test**:
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- **Kolmogorov - Smirnov test**
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compatibility between expected and empirical CDF
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compatibility between expected and empirical CDF
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. . .
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. . .
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- **Trapani test**:
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- **Trapani test**
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test for finite or infinite moments
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test for finite or infinite moments
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@ -29,6 +29,8 @@ How to estimate sample median, mode and FWHM?
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\End{block}
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\End{block}
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. . .
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\setbeamercovered{}
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\setbeamercovered{}
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\begin{center}
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\begin{center}
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\begin{tikzpicture}[remember picture, >=Stealth]
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\begin{tikzpicture}[remember picture, >=Stealth]
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@ -139,7 +141,7 @@ How to estimate sample median, mode and FWHM?
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\begin{center}
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\begin{center}
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\begin{tikzpicture}[remember picture, overlay]
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\begin{tikzpicture}[remember picture, overlay]
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% region
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% region
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\draw [cyclamen, ultra thick] (f1) -- (f2);
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\draw [ultra thick] (f1) -- (f2);
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\end{tikzpicture}
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\end{tikzpicture}
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\end{center}
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\end{center}
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@ -145,7 +145,8 @@ $$
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If $a_j$ uniformly distributed:
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If $a_j$ uniformly distributed:
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- $\zeta_j (u)$ Bernoulli PDF with $P\left( \zeta_j (u) = 1 \right) = \frac{1}{2}$
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- $\zeta_j (u)$ Bernoulli PDF with $P\left( \zeta_j (u) = 1 \right) = \frac{1}{2}$
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$\hence E[\zeta_j]_j = \frac{1}{2} \quad \wedge \quad V[\zeta_j]_j = \frac{1}{4}$
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$\hence \text{E}[\zeta_j]_j = \frac{1}{2}
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\quad \wedge \quad \text{Var}[\zeta_j]_j = \frac{1}{4}$
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## Trapani test
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## Trapani test
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