Levy statistics

Ebook Atoms in electromagnetic fields (Second edition): Part 2 includes contents: Atoms in high frequency fields or in the vacuum field simple physical pictures for radiative corrections, sisyphus cooling and subrecoil cooling, levy statistics and laser cooling,...

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Stable laws { also called -stable or Levy-stable { are a rich family of probability distributions that allow skewness and heavy tails and have many interesting mathematical properties. They appear in the context of the Generalized Central Limit Theorem which states that the only possible non-trivial limit of normalized sums of independent identically distributed variables is -stable. The Standard Central Limit Theorem states that the limit of normalized sums of independent identically distributed terms with nite variance is Gaussian (-stable with  = 2).

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The large loss effect that we report reinforces the findings of Kamstra, Kramer, and Levi (2000), who document a stock market effect of similar magnitude in response to the daylight saving clock change. While Pinegar (2002) argues that the “daylight saving anomaly” is sensitive to outliers, our effect remains economically and statistically significant even after removing outliers in the data and applying a number of robustness checks. Another contribution of this paper is that we are able to go a long way towards addressing the main disadvantage of the event approach.

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