Algorithm AS 84: Measures of Multivariate Skewness and Kurtosis

Mardia, Kanti V.; Zemroch, P. J.

doi:10.2307/2346576

Cited by 87 publications

(48 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…changes in the spatial position of the bacterium in three-dimensional space between two different time instances) obtained from the bacterium trajectory obey a multivariable normal distribution in the three-dimensional environment. Non-zero skewness shows that the probability density function of motion increment does not follow the normal distribution and this is a signature of nonlinearity [ 72 ].…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Multi-fractal characterization of bacterial swimming dynamics: a case study on real and simulatedSerratia marcescens

et al. 2017

View full text Add to dashboard Cite

To add to the current state of knowledge about bacterial swimming dynamics, in this paper, we study the fractal swimming dynamics of populations of Serratia marcescens bacteria both in vitro and in silico, while accounting for realistic conditions like volume exclusion, chemical interactions, obstacles and distribution of chemoattractant in the environment. While previous research has shown that bacterial motion is non-ergodic, we demonstrate that, besides the non-ergodicity, the bacterial swimming dynamics is multi-fractal in nature. Finally, we demonstrate that the multi-fractal characteristic of bacterial dynamics is strongly affected by bacterial density and chemoattractant concentration.

show abstract

Section: Resultsmentioning

confidence: 99%

“…Using the Mardia method [72][73][74], we measured the multivariate skewness of our data for simulated bacteria (see electronic supplementary material, equation ( 2)). The non-zero highly variable skewness plots demonstrate that bacterial motion cannot be modelled by a multivariable normal distribution for all the cases under consideration (i.e.…”

Section: Resultsmentioning

confidence: 99%

Multi-fractal characterization of bacterial swimming dynamics: a case study on real and simulatedSerratia marcescens

et al. 2017

View full text Add to dashboard Cite

show abstract

“…Second, a "bulge" is apparent in the distribution in the region around PC1 = -1.5, PC2 = -0.5 associated with strong southward-shifted jets. One quantitative measure of the deviation of the data from Gaussianity is the multivariate skewness of Mardia and Zemroch [1975]. The multivariate skewness of the ERA-40 data sample is 0.198.…”

Section: Frequency and Persistence Of The Jetmentioning

confidence: 99%

Flow‐dependent predictability of the North Atlantic jet

Frame

Methven

Gray

et al. 2013

Geophysical Research Letters

View full text Add to dashboard Cite

The North Atlantic eddy‐driven jet is a major component of the large‐scale flow in the northern hemisphere. Here we present evidence from reanalysis and ensemble forecast data for systematic flow‐dependent predictability of the jet during northern hemisphere winter (DJF). It is found that when the jet is weakened or split, it is both less persistent and less predictable. The lack of predictability manifests itself as the onset of an anomalously large instantaneous rate of spread of ensemble forecast members as the jet becomes weakened. This suggests that, as the jet weakens or splits, it enters into a state more sensitive to small differences between ensemble forecast members, rather like the sensitive region between the wings of the Lorenz attractor.

show abstract

“…In the analytical and semi-analytical approaches, moment errors , N j θ are assumed to follow a certain parametric distribution that can be multivariate Gaussian as in (31), based on a given bias-covariance matrix modeling or a more sophisticated approach taking into account the natural bounds of the simulated moments , (7) and constitute an alternative to the use of algebraic deviations of moments from those given by the bivariate Gaussian (e.g., bivariate cumulants) [40].…”

Section: Significance Tests Of the Gaussian And Non-gaussian MImentioning

confidence: 99%

Minimum Mutual Information and Non-Gaussianity through the Maximum Entropy Method: Estimation from Finite Samples

Pires

Perdigão

2013

Entropy

View full text Add to dashboard Cite

Abstract:The Minimum Mutual Information (MinMI) Principle provides the least committed, maximum-joint-entropy (ME) inferential law that is compatible with prescribed marginal distributions and empirical cross constraints. Here, we estimate MI bounds (the MinMI values) generated by constraining sets T cr comprehended by m cr linear and/or nonlinear joint expectations, computed from samples of N iid outcomes. Marginals (and their entropy) are imposed by single morphisms of the original random variables.N-asymptotic formulas are given both for the distribution of cross expectation's estimation errors, the MinMI estimation bias, its variance and distribution. A growing T cr leads to an increasing MinMI, converging eventually to the total MI. Under N-sized samples, the MinMI increment relative to two encapsulated sets T cr1  T cr2 (with numbers of constraints As an example, we have set marginals to being normally distributed (Gaussian) and have built a sequence of MI bounds, associated to successive non-linear correlations due to joint non-Gaussianity. Noting that in real-world situations available sample sizes can be rather low, the relationship between MinMI bias, probability density over-fitting and outliers is put in evidence for under-sampled data. OPEN ACCESSEntropy 2013, 15 722

show abstract

Algorithm AS 84: Measures of Multivariate Skewness and Kurtosis

Cited by 87 publications

References 3 publications

Multi-fractal characterization of bacterial swimming dynamics: a case study on real and simulatedSerratia marcescens

Multi-fractal characterization of bacterial swimming dynamics: a case study on real and simulatedSerratia marcescens

Flow‐dependent predictability of the North Atlantic jet

Minimum Mutual Information and Non-Gaussianity through the Maximum Entropy Method: Estimation from Finite Samples

Contact Info

Product

Resources

About