Kurtosis is a descriptive statistic used to help measure how data disperse between a distribution's center and tails, with larger values indicating a data distribution may have “heavy” tails that are thickly concentrated with observations or that are long with extreme observations. A distribution's kurtosis can be calculated using different ...

Feb 6, 2010 · Kurtosis is the degree of peakedness of a distribution, usually taken relative to a normal distribution. A distribution having a relatively high peak such as the curve of Fig. 3.2(a) is called leptokurtic, while the curve of Fig. 3.2(b), which is flat-topped, is called platykurtic.

Kurtosis (or, more accurately, the excess kurtosis) is a mathematical term that measures how much a distribution deviates from being Gaussian. Kurtosis can be measured directly from an estimated displacement function, though another way to estimate it that requires fewer measurements is to deconstruct the signal from multiple b-values and ...

On kurtosis of surface elevation. A strong link between increasing kurtosis and increasing freak wave occurrence was established by Mori and Janssen (2006), and hence, it has been used in the studies of crossing seas as a proxy for the occurrence of rogue waves.

Jan 15, 2025 · Aiming at solving the limitation, a novel maximum L-Kurtosis deconvolution (MLKD) algorithm is proposed. Firstly, the L-Kurtosis is introduced, and the results show that it remains approximately unchanged for different outliers. This characteristic of the L-Kurtosis is the keystone for the proposed deconvolution algorithm.

The coefficient of kurtosis (or also excess kurtosis or just excess) is used to assess whether a density is more or less peaked around its center, than the density of a normal curve and negative values are sometimes used to indicate that a density is flattered around its center than the density of a normal curve. The normal curve has zero value ...

Jan 1, 2016 · Kurtosis is a measure of peakedness, and hence it is a good indicator of signal impulsiveness in the context of fault detection for rotating components. Kurtosis is expressed as (1) k u r t o s i s (x) = E {(x − μ) 4} σ 4 − 3 where μ and σ are the mean and standard deviation of time series x, respectively, while E {⋅} is the ...

Mar 1, 2012 · However, any of these studies pay attention to the recovery of the kurtosis of the sample distribution. If, as asserted by Mantegna et al. [34], the idea is to contribute to the search for a model providing optimal description of financial markets, the inevitable conclusion is that the distributions employed for the adjustment must be capable not only of successfully completing …

Nov 1, 2019 · Kurtosis measures the fatness of tails in the return distribution. Risk-averse investors may not be willing to hold assets with higher idiosyncratic kurtosis if there is a greater likelihood of achieving an extremely high or low return in any given time. Assets with higher idiosyncratic kurtosis will command higher premia by investors.

Jun 1, 2018 · Therefore, the reference curve of the standard definition of kurtosis is a Gaussian, but it can easily be seen that he made no attempt to compare two non-Gaussian distributions using their kurtosis values. Following the introduction by Pearson in 1905, the kurtosis has become a notion which is widely encountered in many textbooks.