What is a positively skewed distribution

Why is left distortion called negatively distorted and right distortion called positively distorted?


I am curious about the nomenclature: why is left distortion labeled negatively distorted and right distortion labeled positively distorted?


Reply:


My short answer is that it is by design. The skewness measures are usually constructed so that the positive skewness indicates right-skewed distributions.

Nowadays, the most common measure of skewness, which is usually also taught in schools, is based on the third central moment equation as follows:

μ3 = E. [(X.- μ) 3]]

Take a look at the expression above. If there is more weight (of the distribution function) to the right of the mean, then (x - μ) 3 more positive values ​​at. The right of the mean is positive because and the left is negative because x <μx> μx <μ. So mechanically it seems to answer your question exactly.

However, as @Nick Cox pointed out, there is more than one measure of skewness, like the first Pearson based on the difference m e a n - m o d e a n - m o de. Perhaps different degrees of skewness can lead to different relationships between positive skewness and the tendency to have heavier tails on the right.

Hence, it is interesting to examine why these measures of skewness were introduced in the first place and why they have their specific formulations.

In this context it is useful to consider Yule's representation of skewness in An Introduction to the Theory of Statistics (1912). In the following excerpt he describes the desired properties a reasonable measure of skewness. Basically, it requires that the positive skewness corresponds to the right-angled distributions, as in your picture:






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