![]() The thick-tail distributions have heights higher than a standard normal.Ī straight line sits at the peak of the standard normal. Then, three thick-tailed distributions are overlaid on that standard normal. The figure is based on a standard normal. It is not a distribution on its way to achieving normality. The distribution has already achieved normality. Once the data actually achieves normality, the height of the distribution falls, typically, to a value of 0.4. As the sample size increases, the height of distribution decreases. ![]() That distribution has a peak at some height. As a line, there is no probability, but as we sample the line becomes an interval, so we begin to have a distribution and probabilities. Then, we sample a sequence of values for that random variable. When we assert the existence of a random variable, a Dirac function produces a vertical line to infinity. From that perspective, I could see that skewed normals happen when the dataset is too small to have achieved normality. I’ve taken a data view, rather than a dataset view. Normal distributions are usually assumed and underly linear regression. Thick tail distributions are unlike normal distributions. Finding the mean and the standard deviation is hard. I came across an article, The dangerous disregard for fat tails in quantitative finance. I’ve been focusing on regression to tails for while now.
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