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  2. Skewness - Wikipedia

    en.wikipedia.org/wiki/Skewness

    Example distribution with positive skewness. These data are from experiments on wheat grass growth. In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. The skewness value can be positive, zero, negative, or undefined.

  3. Skew normal distribution - Wikipedia

    en.wikipedia.org/wiki/Skew_normal_distribution

    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 .

  4. Skew-symmetric graph - Wikipedia

    en.wikipedia.org/wiki/Skew-symmetric_graph

    A skew-symmetric graph may equivalently be defined as the double covering graph of a polar graph or switch graph, [1] which is an undirected graph in which the edges incident to each vertex are partitioned into two subsets. Each vertex of the polar graph corresponds to two vertices of the skew-symmetric graph, and each edge of the polar graph ...

  5. Higher-order statistics - Wikipedia

    en.wikipedia.org/wiki/Higher-order_statistics

    HOS are particularly used in the estimation of shape parameters, such as skewness and kurtosis, as when measuring the deviation of a distribution from the normal distribution. In statistical theory , one long-established approach to higher-order statistics, for univariate and multivariate distributions is through the use of cumulants and joint ...

  6. Unimodality - Wikipedia

    en.wikipedia.org/wiki/Unimodality

    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.

  7. Normal distribution - Wikipedia

    en.wikipedia.org/wiki/Normal_distribution

    In the bottom-right graph, smoothed profiles of the previous graphs are rescaled, superimposed and compared with a normal distribution (black curve). Main article: Central limit theorem The central limit theorem states that under certain (fairly common) conditions, the sum of many random variables will have an approximately normal distribution.

  8. Nonparametric skew - Wikipedia

    en.wikipedia.org/wiki/Nonparametric_skew

    A simple example illustrating these relationships is the binomial distribution with n = 10 and p = 0.09. [35] This distribution when plotted has a long right tail. The mean (0.9) is to the left of the median (1) but the skew (0.906) as defined by the third standardized moment is positive. In contrast the nonparametric skew is -0.110.

  9. D'Agostino's K-squared test - Wikipedia

    en.wikipedia.org/wiki/D'Agostino's_K-squared_test

    The sample skewness g 1 and kurtosis g 2 are both asymptotically normal. However, the rate of their convergence to the distribution limit is frustratingly slow, especially for g 2 . For example even with n = 5000 observations the sample kurtosis g 2 has both the skewness and the kurtosis of approximately 0.3, which is not negligible.

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