The Meaning of Kurtosis: Darlington Reexamined

Moors, J.J.A.

doi:10.1080/00031305.1986.10475415

Cited by 155 publications

(87 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Finecan (1964) and Moors (1986) showed that kurtosis may be interpreted as measuring the shift of probability mass away from Ϯ toward either the middle of the distribution or the tails, the latter case giving rise to fat-tailed distributions (see also Balanda and MacGillivray 1988 for a useful discussion). Moreover, the kurtosis ␥ 2 (F) maintains a stochastic ordering of distribution in the sense that F ՞ G if ␥ 2 (F) Յ ␥ 2 (G).…”

Section: Remarkmentioning

confidence: 97%

Contaminated Exponential Dispersion Loss Models

Landsman

Makov

2003

North American Actuarial Journal

View full text Add to dashboard Cite

show abstract

Section: Remarkmentioning

confidence: 97%

Contaminated Exponential Dispersion Loss Models

Landsman

Makov

2003

North American Actuarial Journal

View full text Add to dashboard Cite

show abstract

“…We note that excess kurtosis, κ e (which, as noted previously, is proportional to the Binder cumulant, U 4 = −κ e /3, for non-periodic random variables) has long been considered as a measure for unimodality versus bimodality in statistics literature, where its usefulness and limitations have also been discussed extensively [98][99][100]. In the case of two-point distributions (equivalent to the twostate model introduced in Appendix B), the Binder cumulant can be shown to take large negative values as the distribution becomes less symmetric (i.e., as the probability density at one of the points or, equivalently, the bimodal ratio, R Ψ , is decreased), and, eventually, tend to negative infinity as the onset of bimodality is approached (R Ψ → 0) [98].…”

Section: F Onset Of Population Splitting: Binder Cumulantmentioning

confidence: 99%

Population splitting of rodlike swimmers in Couette flow

et al. 2017

View full text Add to dashboard Cite

We present a quantitative analysis on the response of a dilute active suspension of self-propelled rods (swimmers) in a planar channel subjected to an imposed shear flow. To best capture the salient features of shear-induced effects, we consider the case of an imposed Couette flow, providing a constant shear rate across the channel. We argue that the steady-state behavior of swimmers can be understood in the light of a population splitting phenomenon, occurring as the shear rate exceeds a certain threshold, initiating the reversal of swimming direction for a finite fraction of swimmers from down-to upstream or vice versa, depending on swimmer position within the channel. Swimmers thus split into two distinct, statistically significant and oppositely swimming majority and minority populations. The onset of population splitting translates into a transition from a self-propulsiondominated regime to a shear-dominated regime, corresponding to a unimodal-to-bimodal change in the probability distribution function of the swimmer orientation. We present a phase diagram in terms of the swim and flow Péclet numbers showing the separation of these two regimes by a discontinuous transition line. Our results shed further light on the behavior of swimmers in a shear flow and provide an explanation for the previously reported non-monotonic behavior of the mean, near-wall, parallel-to-flow orientation of swimmers with increasing shear strength.

show abstract

“…and is more difficult (Havilcek and Crain, 1988;Moors, 1986;Chissan, 1970) to interpret. It is a statistical measure of the concentration of the distribution around the mean.…”

Section: Moments Of a Random Variable: Skewness And Kurtosismentioning

confidence: 97%

Fitting Straight Lines with Replicated Observations by Linear Regression. IV. Transforming Data

Asuero

Bueno

2011

Critical Reviews in Analytical Chemistry

View full text Add to dashboard Cite

By transforming variables it is possible to introduce non-linear terms to the mathematical framework of linear regression. The purpose of this article is to stress the importance of transforming data in the context of linear regression analysis. However, often problems arise when people unfamiliar with mathematical statistics attempt to put this theory into practice for a certain application. Reasons for making transformations, probability plots and normality, transformations to simplify relationships, and weighting transformation data are covered in this paper. Special attention has also been paid to the Box-Cox method, i.e., transformation based on sample data observations, which is very easy to apply in practice despite its mathematical background. Statistical measurements are also re-expressed after data transformation, and a number of applications concerning the use of transformation and variance stabilization in analytical chemistry are given in tabular form. The analytical, pharmaceutical, biochemical, and clinical literature has been thoroughly revised. Variance analysis and applications on fitting straight lines with replicated observations by linear regression will be the subject of the later paper of the series.

show abstract

The Meaning of Kurtosis: Darlington Reexamined

Cited by 155 publications

References 7 publications

Contaminated Exponential Dispersion Loss Models

Contaminated Exponential Dispersion Loss Models

Population splitting of rodlike swimmers in Couette flow

Fitting Straight Lines with Replicated Observations by Linear Regression. IV. Transforming Data

Contact Info

Product

Resources

About