What is crookedness

Crookedness

Dictionary

Crookedness is a measure of the asymmetry of a distribution. It is defined from −∞ to + ∞, whereby a value of zero would not indicate a symmetrical distribution (without skewness).Left skew (identical to the term right part) Distributions have negative skewness while crooked (left part) distributions have positive skewness. Any nonsymmetrical distribution is skewed. (These rules only apply to unimodal distributions.)

Right-skewed distributions are common when using a variable on the left is limitedbut not on the right. This is the case, for example, for variables that have a natural zero point (e.g. for variables that measure time, such as reaction times). Many financial variables (e.g. income, market value, prices) also have a natural zero point and are usually skewed to the right.

Left skewed distributions occur less often than right skew. Bounded variables that are closer to their maximum will mostly have a left skewed distribution. This could be the case, for example, with a simple test. Most of the results will be closer to 100%, so the distribution will be skewed to the left.

Known right-skewed distributions are the Poisson distribution, χ² distribution, exponential distribution, logarithmic normal distribution and all distributions belonging to the gamma distribution family. Left skewed distributions are found less often. However, there are a number of distribution functions that can be skewed to the left or to the right, depending on which parameters are selected. Well-known distributions of this type are the binomial distribution and the beta distribution. Distributions that are neither skewed to the left nor to the right are symmetrical. Known symmetric distributions are the normal distribution, t-Distribution, logistic distribution and uniform distribution.

Transformations

For statistical purposes it is often necessary to transform distributions in order to make them more symmetrical. For right-skewed distribution It is recommended - depending on the degree of skewness - to correct roots, logarithms or reciprocal values ​​(ascending according to the degree of correction).

To aleft-skewed distribution To make it more symmetrical, powers can be used (e.g., squaring). The higher the potency, the stronger the correction.