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- Kurtosis abstract "In probability theory and statistics, kurtosis (from Greek: κυρτός, kyrtos or kurtos, meaning "curved, arching") is any measure of the "peakedness" of the probability distribution of a real-valued random variable. In a similar way to the concept of skewness, kurtosis is a descriptor of the shape of a probability distribution and, just as for skewness, there are different ways of quantifying it for a theoretical distribution and corresponding ways of estimating it from a sample from a population. There are various interpretations of kurtosis, and of how particular measures should be interpreted; these are primarily peakedness (width of peak), tail weight, and lack of shoulders (distribution primarily peak and tails, not in between).One common measure of kurtosis, originating with Karl Pearson, is based on a scaled version of the fourth moment of the data or population, but it has been argued that this really measures heavy tails, and not peakedness. For this measure, higher kurtosis means more of the variance is the result of infrequent extreme deviations, as opposed to frequent modestly sized deviations.The kurtosis of any univariate normal distribution is 3. It is common to compare the kurtosis of a distribution to this value. Distribution with kurtosis less than 3 are said to be platykurtic. An example of a platykurtic distribution is the uniform distribution, which does not have positive-valued tails. Distributions with kurtosis greater than 3 are said to be leptokurtic. An example of a leptokurtic distribution is the Laplace distribution, which has tails that asymptotically approach zero more slowly than a Gaussian. It is also common practice to use an adjusted version of Pearson's kurtosis, the excess kurtosis, which is the kurtosis minus 3, to provide the comparison to the normal distribution. Some authors use "kurtosis" by itself to refer to the excess kurtosis. For the reason of clarity and generality, however, this article follows the non-excess convention and explicitly indicates where excess kurtosis is meant.Alternative measures of kurtosis are: the L-kurtosis, which is a scaled version of the fourth L-moment; measures based on 4 population or sample quantiles. These correspond to the alternative measures of skewness that are not based on ordinary moments.".
- Kurtosis thumbnail KurtosisChanges.png?width=300.
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- Kurtosis wikiPageWikiLink Bernoulli_distribution.
- Kurtosis wikiPageWikiLink Bias_of_an_estimator.
- Kurtosis wikiPageWikiLink Biased_estimator.
- Kurtosis wikiPageWikiLink Binomial_coefficient.
- Kurtosis wikiPageWikiLink Binomial_distribution.
- Kurtosis wikiPageWikiLink Category:Statistical_deviation_and_dispersion.
- Kurtosis wikiPageWikiLink Category:Theory_of_probability_distributions.
- Kurtosis wikiPageWikiLink Central_moment.
- Kurtosis wikiPageWikiLink Coin_flipping.
- Kurtosis wikiPageWikiLink Coin_toss.
- Kurtosis wikiPageWikiLink Cokurtosis.
- Kurtosis wikiPageWikiLink Cumulant.
- Kurtosis wikiPageWikiLink DAgostinos_K-squared_test.
- Kurtosis wikiPageWikiLink Deviation_(statistics).
- Kurtosis wikiPageWikiLink Exponential_distribution.
- Kurtosis wikiPageWikiLink Exponential_power_distribution.
- Kurtosis wikiPageWikiLink Fat-tailed_distribution.
- Kurtosis wikiPageWikiLink Generalized_normal_distribution.
- Kurtosis wikiPageWikiLink Goodness-of-fit.
- Kurtosis wikiPageWikiLink Goodness_of_fit.
- Kurtosis wikiPageWikiLink Heavy-tailed_distribution.
- Kurtosis wikiPageWikiLink Hyperbolic_secant_distribution.
- Kurtosis wikiPageWikiLink Intensive_and_extensive_properties.
- Kurtosis wikiPageWikiLink Jarque–Bera_test.
- Kurtosis wikiPageWikiLink Karl_Pearson.
- Kurtosis wikiPageWikiLink Kurtosis_risk.
- Kurtosis wikiPageWikiLink L-kurtosis.
- Kurtosis wikiPageWikiLink L-moment.
- Kurtosis wikiPageWikiLink Laplace_distribution.
- Kurtosis wikiPageWikiLink Logistic_distribution.
- Kurtosis wikiPageWikiLink MATLAB.
- Kurtosis wikiPageWikiLink Maple.
- Kurtosis wikiPageWikiLink Mathematica.
- Kurtosis wikiPageWikiLink Matlab.
- Kurtosis wikiPageWikiLink Mean.
- Kurtosis wikiPageWikiLink Microsoft_Excel.
- Kurtosis wikiPageWikiLink Moment_(mathematics).
- Kurtosis wikiPageWikiLink Moment_(statistics).
- Kurtosis wikiPageWikiLink Moment_about_the_mean.
- Kurtosis wikiPageWikiLink Negative_number.
- Kurtosis wikiPageWikiLink Normal_distribution.
- Kurtosis wikiPageWikiLink Normality_test.
- Kurtosis wikiPageWikiLink NumPy.
- Kurtosis wikiPageWikiLink Parabola.
- Kurtosis wikiPageWikiLink Parameter.
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- Kurtosis wikiPageWikiLink Pearson_distribution.
- Kurtosis wikiPageWikiLink Poisson_distribution.
- Kurtosis wikiPageWikiLink Positive_number.
- Kurtosis wikiPageWikiLink Probability_distribution.
- Kurtosis wikiPageWikiLink Probability_theory.
- Kurtosis wikiPageWikiLink Quantile.
- Kurtosis wikiPageWikiLink Quantiles.
- Kurtosis wikiPageWikiLink R_(programming_language).
- Kurtosis wikiPageWikiLink Raised_cosine_distribution.
- Kurtosis wikiPageWikiLink Random_variable.
- Kurtosis wikiPageWikiLink Rayleigh_distribution.
- Kurtosis wikiPageWikiLink Real_line.
- Kurtosis wikiPageWikiLink Real_number.
- Kurtosis wikiPageWikiLink Sample_(statistics).
- Kurtosis wikiPageWikiLink Sample_mean.
- Kurtosis wikiPageWikiLink Sample_mean_and_sample_covariance.
- Kurtosis wikiPageWikiLink Sample_variance.
- Kurtosis wikiPageWikiLink Scale_parameter.
- Kurtosis wikiPageWikiLink Shape_parameter.
- Kurtosis wikiPageWikiLink Sign_(mathematics).
- Kurtosis wikiPageWikiLink Skewness.
- Kurtosis wikiPageWikiLink Standard_deviation.
- Kurtosis wikiPageWikiLink Standardized_moment.
- Kurtosis wikiPageWikiLink Statistics.
- Kurtosis wikiPageWikiLink Students_t-distribution.
- Kurtosis wikiPageWikiLink Support_(mathematics).
- Kurtosis wikiPageWikiLink Tensor.
- Kurtosis wikiPageWikiLink Turbulence.
- Kurtosis wikiPageWikiLink Uniform_distribution_(continuous).
- Kurtosis wikiPageWikiLink Uniform_distribution_(discrete).
- Kurtosis wikiPageWikiLink Unimodal.
- Kurtosis wikiPageWikiLink Unimodality.
- Kurtosis wikiPageWikiLink Variance.
- Kurtosis wikiPageWikiLink Wigner_semicircle_distribution.
- Kurtosis wikiPageWikiLink File:1909_US_Penny.jpg.
- Kurtosis wikiPageWikiLink File:KurtosisChanges.png.
- Kurtosis wikiPageWikiLink File:Pearson_type_VII_distribution_PDF.png.
- Kurtosis wikiPageWikiLink File:Pearson_type_VII_distribution_log-PDF.png.
- Kurtosis wikiPageWikiLink File:Standard_symmetric_pdfs.png.
- Kurtosis wikiPageWikiLink File:Standard_symmetric_pdfs_logscale.png.
- Kurtosis wikiPageWikiLinkText "Kurtosis".