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English: Diagrams illustrating negative and positive skew. (Created with Inkscape , an Open Source software, and based on the previous PNG version en:File:Skew.png with the text removed.) Date
The skewness value can be positive, zero, negative, or undefined. For a unimodal distribution (a distribution with a single peak), negative skew commonly indicates that the tail is on the left side of the distribution, and positive skew indicates that the tail is on the right. In cases where one tail is long but the other tail is fat, skewness ...
The nucleotide composition skew spectra ranges from −1, which corresponds to G = 0 or A = 0, to +1, which corresponds to T= 0 or C = 0. [2] Therefore, positive GC skew represents richness of G over C and the negative GC skew represents richness of C over G.
The accompanying plot of skewness as a function of variance and mean shows that maximum variance (1/4) is coupled with zero skewness and the symmetry condition (μ = 1/2), and that maximum skewness (positive or negative infinity) occurs when the mean is located at one end or the other, so that the "mass" of the probability distribution is ...
This can also be seen as a three-parameter generalization of a normal distribution to add skew; another distribution like that is the skew normal distribution, which has thinner tails. The distribution is a compound probability distribution in which the mean of a normal distribution varies randomly as a shifted exponential distribution .
When the smaller values tend to be farther away from the mean than the larger values, one has a skew distribution to the left (i.e. there is negative skewness), one may for example select the square-normal distribution (i.e. the normal distribution applied to the square of the data values), [1] the inverted (mirrored) Gumbel distribution, [1 ...
The exponentially modified normal distribution is another 3-parameter distribution that is a generalization of the normal distribution to skewed cases. The skew normal still has a normal-like tail in the direction of the skew, with a shorter tail in the other direction; that is, its density is asymptotically proportional to for some positive .
This does not look random, but it satisfies the definition of random variable. This is useful because it puts deterministic variables and random variables in the same formalism. The discrete uniform distribution, where all elements of a finite set are equally likely. This is the theoretical distribution model for a balanced coin, an unbiased ...