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The distribution is said to be left-skewed, left-tailed, or skewed to the left, despite the fact that the curve itself appears to be skewed or leaning to the right; left instead refers to the left tail being drawn out and, often, the mean being skewed to the left of a typical center of the data.
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 .
The Laplace distribution; The Lévy skew alpha-stable distribution or stable distribution is a family of distributions often used to characterize financial data and critical behavior; the Cauchy distribution, Holtsmark distribution, Landau distribution, Lévy distribution and normal distribution are special cases. The Linnik distribution
In this manner, a distribution that is skewed to the right is transformed into a distribution that is skewed to the left and vice versa. Example . The F-expression of the positively skewed Gumbel distribution is: F=exp[-exp{-( X - u )/0.78 s }], where u is the mode (i.e. the value occurring most frequently) and s is the standard deviation .
The distribution should not be confused with the skew normal distribution or another asymmetric version. Indeed, the distribution here is a special case of a bi-Gaussian, whose left and right widths are proportional to 1 − λ {\displaystyle 1-\lambda } and 1 + λ {\displaystyle 1+\lambda } .
Letting α = β in the above expression one obtains γ 1 = 0, showing once again that for α = β the distribution is symmetric and hence the skewness is zero. Positive skew (right-tailed) for α < β, negative skew (left-tailed) for α > β. Using the parametrization in terms of mean μ and sample size ν = α + β:
The asymmetric generalized normal distribution can be used to model values that may be normally distributed, or that may be either right-skewed or left-skewed relative to the normal distribution. The skew normal distribution is another distribution that is useful for modeling deviations from normality due to skew. Other distributions used to ...
The Gompertz distribution is a flexible distribution that can be skewed to the right and to the left. Its hazard function = is a convex function of (;,).The model can be fitted into the innovation-imitation paradigm with = as the coefficient of innovation and as the coefficient of imitation.