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  2. Kurtosis - Wikipedia

    en.wikipedia.org/wiki/Kurtosis

    Larger kurtosis indicates a more serious outlier problem, and may lead the researcher to choose alternative statistical methods. D'Agostino's K-squared test is a goodness-of-fit normality test based on a combination of the sample skewness and sample kurtosis, as is the Jarque–Bera test for normality.

  3. Skewness - Wikipedia

    en.wikipedia.org/wiki/Skewness

    The normal distribution has a skewness of zero. But in reality, data points may not be perfectly symmetric. So, an understanding of the skewness of the dataset indicates whether deviations from the mean are going to be positive or negative. D'Agostino's K-squared test is a goodness-of-fit normality test based on sample skewness and sample kurtosis.

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

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

    In the following, { x i } denotes a sample of n observations, g 1 and g 2 are the sample skewness and kurtosis, m j ’s are the j-th sample central moments, and ¯ is the sample mean. Frequently in the literature related to normality testing, the skewness and kurtosis are denoted as √ β 1 and β 2 respectively.

  5. Fat-tailed distribution - Wikipedia

    en.wikipedia.org/wiki/Fat-tailed_distribution

    A fat-tailed distribution is a probability distribution that exhibits a large skewness or kurtosis, relative to that of either a normal distribution or an exponential distribution. [when defined as?] In common usage, the terms fat-tailed and heavy-tailed are sometimes synonymous; fat-tailed is sometimes also defined as a subset of heavy-tailed ...

  6. 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 .

  7. Shape of a probability distribution - Wikipedia

    en.wikipedia.org/wiki/Shape_of_a_probability...

    The shape of a distribution may be considered either descriptively, using terms such as "J-shaped", or numerically, using quantitative measures such as skewness and kurtosis.

  8. Kurtosis risk - Wikipedia

    en.wikipedia.org/wiki/Kurtosis_risk

    Kurtosis risk applies to any kurtosis-related quantitative model that assumes the normal distribution for certain of its independent variables when the latter may in fact have kurtosis much greater than does the normal distribution. Kurtosis risk is commonly referred to as "fat tail" risk. The "fat tail" metaphor explicitly describes the ...

  9. Probability distribution fitting - Wikipedia

    en.wikipedia.org/wiki/Probability_distribution...

    When the larger values tend to be farther away from the mean than the smaller values, one has a skew distribution to the right (i.e. there is positive skewness), one may for example select the log-normal distribution (i.e. the log values of the data are normally distributed), the log-logistic distribution (i.e. the log values of the data follow ...