Lack of small tibial component size availability for females in a highly utilized total knee arthroplasty system
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Kurtosis
A computer system for simulation of quantitative twin data is being developed. The capability is being built in to simulate distributions with known means, standard deviations, skewness and kurtosis.
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Population mean
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This study introduces the bucket plot, a visual tool to detect skewness and kurtosis in a continuously distributed random variable. The plot can be applied to both moment and centile skewness and kurtosis. The bucket plot is used to detect skewness and kurtosis either in a response variable, or in the residuals from a fitted model as a diagnostic tool by which to assess the adequacy of a fitted distribution to the response variable regarding skewness and kurtosis. We demonstrate the bucket plot in nine simulated skewness and kurtosis scenarios, and the usefulness of the plot is shown in a real-data situation.
Kurtosis
Plot (graphics)
Central moment
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The Mardia measures of multivariate skewness and kurtosis summarize the respective characteristics of a multivariate distribution with two numbers. However, these measures do not reflect the sub-dimensional features of the distribution. Consequently, testing procedures based on these measures may fail to detect skewness or kurtosis present in a sub-dimension of the multivariate distribution. We introduce sub-dimensional Mardia measures of multivariate skewness and kurtosis, and investigate the information they convey about all sub-dimensional distributions of some symmetric and skewed families of multivariate distributions. The maxima of the sub-dimensional Mardia measures of multivariate skewness and kurtosis are considered, as these reflect the maximum skewness and kurtosis present in the distribution, and also allow us to identify the sub-dimension bearing the highest skewness and kurtosis. Asymptotic distributions of the vectors of sub-dimensional Mardia measures of multivariate skewness and kurtosis are derived, based on which testing procedures for the presence of skewness and of deviation from Gaussian kurtosis are developed. The performances of these tests are compared with some existing tests in the literature on simulated and real datasets.
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Shape parameter
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An efficient numerical method for calculation of the sea surface skewness and kurtosis for arbitrary wave spectra, taking up to third-order nonlinear effects into account, is developed. The skewness and kurtosis are calculated for a large number of sea states, covering a wide range of sea-state parameters in terms of wave steepness, water depth, directional spreading and frequency bandwidth. The results are used to propose new accurate expressions for skewness and kurtosis, valid over a wide range of sea states. Existing expressions for skewness and kurtosis reported in the literature are reviewed, and their accuracy is evaluated. Comparison to model-test results and phase-resolved numerical simulation are presented. It is suggested that the new improved parametrizations for skewness and kurtosis, which include dependence on wave steepness, water depth, spectral bandwidth and directional spreading, represent a convenient way to include these covariates into higher-order distributions for crest heights, wave heights and surface elevation.
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Crest
Parametrization (atmospheric modeling)
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This paper explores the ability of some popular income distributions to model observed skewness and kurtosis. We present the generalized beta type 1 (GB1) and type 2 (GB2) distributions' skewness–kurtosis spaces and clarify and expand on previously known results on other distributions' skewness–kurtosis spaces. Data from the Luxembourg Income Study are used to estimate sample moments and explore the ability of the generalized gamma, Dagum, Singh–Maddala, beta of the first kind, beta of the second kind, GB1, and GB2 distributions to accommodate the skewness and kurtosis values. The GB2 has the flexibility to accurately describe the observed skewness and kurtosis.
Kurtosis
Generalized beta distribution
Shape parameter
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Summary Theoretical considerations of kurtosis, whether of partial orderings of distributions with respect to kurtosis or of measures of kurtosis, have tended to focus only on symmetric distributions. With reference to historical points and recent work on skewness and kurtosis, this paper defines anti‐skewness and uses it as a tool to discuss the concept of kurtosis in asymmetric univariate distributions. The discussion indicates that while kurtosis is best considered as a property of symmetrised versions of distributions, symmetrisation does not simply remove skewness. Skewness, anti‐skewness and kurtosis are all inter‐related aspects of shape. The Tukey g and h family and the Johnson Su family are considered as examples.
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Univariate
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Skewness can be used in HIF classification with its statistical strength to identify the asymmetry introduced to the current stream by a HIF. Kurtosis is effective in analyzing the tails of a distribution reflecting its outliners. This paper introduces the concept of relative skewness and relative kurtosis as superior computational approaches for detecting HIF induced statistical changes. Relative skewness produced the most conclusive result in identifying a distinct decay in the index of the stream, subsequent to HIFs as low as 0.5 A. The relative kurtosis shows a clear decline in the index of the data stream as soon as fault occurs with the magnitude of the disturbance a factor on how far and how fast the index decays. While skewness and kurtosis are powerful techniques, a blend of techniques is recommended to ensure a secure HIF classification performance incorporating multiple strategies for their discrimination from other long-lasting network transients.
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Kurtosis
Shape parameter
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moments2 calculates various measures of skewness and kurtosis. Based on Nicholas Cox's moments, it also calculates mean and standard deviation for a list of variables. moments2 differs from moments only in allowing different measures of skewness and kurtosis and making the measures used in SAS and SPSS the default.
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