Like skewness, kurtosis describes a particular aspect of a probability distribution. There are different ways to quantify kurtosis for a theoretical...

α → 0 excess kurtosis = lim β → 0 excess kurtosis = lim μ → 0 excess kurtosis = lim μ → 1 excess kurtosis = ∞ lim α → ∞ excess kurtosis = 6 β ,   lim...

the average than is expected for a normal distribution. Kurtosis risk applies to any kurtosis-related quantitative model that assumes the normal distribution...

distribution is 3σ4. The kurtosis κ is defined to be the standardized fourth central moment. (Equivalently, as in the next section, excess kurtosis is the fourth...

and the excess kurtosis being zero. Samples from a normal distribution have an expected skewness of 0 and an expected excess kurtosis of 0 (which is the...

3.5.11. Measures of Skewness and Kurtosis". NIST. Retrieved 18 March 2012. "Measures of Shape: Skewness and Kurtosis", 2008–2016 by Stan Brown, Oak Road...

distributions of the skewness and kurtosis can themselves be analysed in terms of their means μ1, variances μ2, skewnesses γ1, and kurtosis γ2. This has been done...

analogous to standard deviation, skewness and kurtosis, termed the L-scale, L-skewness and L-kurtosis respectively (the L-mean is identical to the conventional...

deviation a measure of the shape of the distribution like skewness or kurtosis if more than one variable is measured, a measure of statistical dependence...

Zsolt István Kürtösi (born 21 March 1971 in Kiskunfélegyháza) is a Hungarian decathlete and bobsledder. Zsolt Kürtösi at World Athletics v t e v t e...

Gaussian signals have zero kurtosis, Super-Gaussian signals have positive kurtosis, and Sub-Gaussian signals have negative kurtosis. The denominator is the...

that (where they exist) the skewness and kurtosis of these distribution are constants, as skewness and kurtosis are independent of location and scale parameters...

truncated mean, it also forms the basis for robust measures of skewness and kurtosis, and even a normality test. Summary statistics Socio-economic decile (for...

Jarque–Bera test is itself derived from skewness and kurtosis estimates. Mardia's multivariate skewness and kurtosis tests generalize the moment tests to the multivariate...

so kurtosis is not a good measure of "peakedness." Examples of such shapes can be found in the kurtosis wiki entry. The Doppler radar kurtosis analysis...

{\gamma ^{2}+1}{\kappa }}} where γ is the skewness and κ is the kurtosis. The kurtosis is here defined to be the standardised fourth moment around the...

case of the binomial distribution with n = 1. {\displaystyle n=1.} The kurtosis goes to infinity for high and low values of p , {\displaystyle p,} but...

deviation (or variance), the minimum and maximum values of the variables, kurtosis and skewness. Descriptive statistics provide simple summaries about the...

deviation but different means, the overall distribution will exhibit low kurtosis relative to a single normal distribution – the means of the sub populations...

distribution is a probability distribution that exhibits a large skewness or kurtosis, relative to that of either a normal distribution or an exponential distribution...

resembles the normal distribution in shape but has heavier tails (higher kurtosis). The logistic distribution is a special case of the Tukey lambda distribution...

cost. An example of the online algorithm for kurtosis implemented as described is: def online_kurtosis(data): n = mean = M2 = M3 = M4 = 0 for x in data:...

4 − 3 {\displaystyle \gamma _{2}=\mu _{4}/\sigma ^{4}-3} is the excess kurtosis. However, one can use other estimators for σ 2 {\displaystyle \sigma ^{2}}...

Friedman. Mardia's test is based on multivariate extensions of skewness and kurtosis measures. For a sample {x1, ..., xn} of k-dimensional vectors we compute...

sample variance, though the optimal scale factor depends on the excess kurtosis of the population (see mean squared error: variance) and introduces bias...

}}\leq {\sqrt {3}}.} Rohatgi and Szekely claimed that the skewness and kurtosis of a unimodal distribution are related by the inequality: γ 2 − κ ≤ 6 5...

characteristics of such a discrete variable (such as the mean, variance, and kurtosis), starting from the formulas given for a continuous distribution of the...

\over \sigma _{X}^{4}}={\operatorname {kurtosis} {\big [}X{\big ]}},} For two random variables, X and Y, the kurtosis of the sum, X + Y, is K X + Y = 1 σ...

Statistical dispersion Central tendency Median Mode Descriptive statistics Kurtosis Law of averages Mean value theorem Moment (mathematics) Summary statistics...

unpaired situation or the sign test for paired situation. Skewness risk and kurtosis risk also have technical implications in calculation of value at risk....