Caudas longas, curtose e risco

O Matt Bogard escreve um pequeno post com essas questões, e aponta algumas referências.

O entendimento do que é Curtose (que é proveniente da estatística) é de fundamental importância em estudos para mensuração de amplitude de valores de uma variável específica; especialmente se esses estudos forem ligados a questões ligadas a probabilidade.

They recommend that kurtosis be defined as “the location- and scale-free movement of probability mass from the shoulders of a distribution into its center and tails. In particular, this definition implies that peakedness and tail weight are best viewed as components [emphasis mine] of kurtosis…. This definition is necessarily vague because the movement can be formalized in many ways” (p. 116). In other words, the peaks and tails of a distribution contribute to the value of the kurtosis, but so do other features.

The tail of the distribution is the most important contributor. Although Balanda and MacGillivray do not mention it, the kurtosis is a non-robust statistic that can be severely influenced by the value of a single outlier. For example, if you choose 999 observations from a normal distribution, the sample kurtosis will be close to 0. However, if you add a single observation that has the value 100, the sample kurtosis jumps to more than 800!