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  2. Skewness - Wikipedia

    en.wikipedia.org/wiki/Skewness

    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 ...

  3. Shape of a probability distribution - Wikipedia

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

    In statistics, the concept of the shape of a probability distribution arises in questions of finding an appropriate distribution to use to model the statistical properties of a population, given a sample from that population.

  4. Box plot - Wikipedia

    en.wikipedia.org/wiki/Box_plot

    Figure 2. Box-plot with whiskers from minimum to maximum Figure 3. Same box-plot with whiskers drawn within the 1.5 IQR value. A boxplot is a standardized way of displaying the dataset based on the five-number summary: the minimum, the maximum, the sample median, and the first and third quartiles.

  5. Data transformation (statistics) - Wikipedia

    en.wikipedia.org/wiki/Data_transformation...

    Thus, when there is evidence of substantial skew in the data, it is common to transform the data to a symmetric distribution [1] before constructing a confidence interval. If desired, the confidence interval for the quantiles (such as the median) can then be transformed back to the original scale using the inverse of the transformation that was ...

  6. Skewed generalized t distribution - Wikipedia

    en.wikipedia.org/wiki/Skewed_generalized_t...

    where is the beta function, is the location parameter, > is the scale parameter, < < is the skewness parameter, and > and > are the parameters that control the kurtosis. and are not parameters, but functions of the other parameters that are used here to scale or shift the distribution appropriately to match the various parameterizations of this distribution.

  7. Method of moments (statistics) - Wikipedia

    en.wikipedia.org/wiki/Method_of_moments_(statistics)

    In statistics, the method of moments is a method of estimation of population parameters.The same principle is used to derive higher moments like skewness and kurtosis. It starts by expressing the population moments (i.e., the expected values of powers of the random variable under consideration) as functions of the parameters of interest.

  8. Shape parameter - Wikipedia

    en.wikipedia.org/wiki/Shape_parameter

    Most simply, they can be estimated in terms of the higher moments, using the method of moments, as in the skewness (3rd moment) or kurtosis (4th moment), if the higher moments are defined and finite. Estimators of shape often involve higher-order statistics (non-linear functions of the data), as in the higher moments, but linear estimators also ...

  9. Kurtosis - Wikipedia

    en.wikipedia.org/wiki/Kurtosis

    The kurtosis is the fourth standardized moment, defined as ⁡ [] = ⁡ [()] = ⁡ [()] (⁡ [()]) =, where μ 4 is the fourth central moment and σ is the standard deviation.Several letters are used in the literature to denote the kurtosis.