# 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 limited**but 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 a**left-skewed distribution** To make it more symmetrical, powers can be used (e.g., squaring). The higher the potency, the stronger the correction.

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