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A histogram is a visual representation of the distribution of quantitative data. ... "skewed left" or "right", "unimodal", "bimodal" or "multimodal". Symmetric, unimodal.
positive skew: The right tail is longer; the mass of the distribution is concentrated on the left of the figure. The distribution is said to be right-skewed, right-tailed, or skewed to the right, despite the fact that the curve itself appears to be skewed or leaning to the left; right instead refers to the right tail being drawn out and, often ...
A bimodal distribution would have two high points rather than one. The shape of a distribution is sometimes characterised by the behaviours of the tails (as in a long or short tail). For example, a flat distribution can be said either to have no tails, or to have short tails.
Values greater than 5/9 may indicate a bimodal or multimodal distribution, though corresponding values can also result for heavily skewed unimodal distributions. [28] The maximum value (1.0) is reached only by a Bernoulli distribution with only two distinct values or the sum of two different Dirac delta functions (a bi-delta 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; The logistic distribution
Rohatgi and Szekely claimed that the skewness and kurtosis of a unimodal distribution are related by the inequality: [13] = where κ is the kurtosis and γ is the skewness. Klaassen, Mokveld, and van Es showed that this only applies in certain settings, such as the set of unimodal distributions where the mode and mean coincide.
Histogram of a sample from a right-skewed distribution – it looks unimodal and skewed right. This is a sample of size 50 from a uniform distribution, plotted as both a histogram, and a normal probability plot.
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 .