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Skewness

About: Skewness is a research topic. Over the lifetime, 5847 publications have been published within this topic receiving 171365 citations.


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TL;DR: In this paper, a bar on the Brazos River near Calvert, Texas, has been analyzed in order to determine the geologic meaning of certain grain size parameters and to study the behavior of the size fractions with transport.
Abstract: A bar on the Brazos River near Calvert, Texas, has been analyzed in order to determine the geologic meaning of certain grain size parameters and to study the behavior of the size fractions with transport. The bar consists of a strongly bimodal mixture of pebble gravel and medium to fine sand; there is a lack of material in the range of 0.5 to 2 mm, because the source does not supply particles of this size. The size distributions of the two modes, which were established in the parent deposits, are nearly invariant over the bar because the present environment of deposition only affects the relative proportions of the two modes, not the grain size properties of the modes themselves. Two proportions are most common; the sediment either contains no gravel or else contains about 60% gravel. Three sediment types with characteristic bedding features occur on the bar in constant stratigraphic order, with the coarsest at the base. Statistical analysis of the data is based on a series of grain size parameters modified from those of Inman (1952) to provide a more detailed coverage of non-normal size curves. Unimodal sediments have nearly normal curves as defined by their skewness and kurtosis. Non-normal kurtosis and skewness values are held to be the identifying characteristics of bimodal sediments even where such modes are not evident in frequency curves. The relative proportions of each mode define a systematic series of changes in numerical properties; mean size, standard deviation and skewness are shown to be linked in a helical trend, which is believed to be applicable to many other sedimentary suites. The equations of the helix may be characteristic of certain environments. Kurtosis values show rhythmic pulsations along the helix and are diagnostic of two-generation sediments.

6,310 citations

Journal ArticleDOI
TL;DR: In this article, the authors developed measures of multivariate skewness and kurtosis by extending certain studies on robustness of the t statistic, and the asymptotic distributions of the measures for samples from a multivariate normal population are derived and a test for multivariate normality is proposed.
Abstract: SUMMARY Measures of multivariate skewness and kurtosis are developed by extending certain studies on robustness of the t statistic. These measures are shown to possess desirable properties. The asymptotic distributions of the measures for samples from a multivariate normal population are derived and a test of multivariate normality is proposed. The effect of nonnormality on the size of the one-sample Hotelling's T2 test is studied empirically with the help of these measures, and it is found that Hotelling's T2 test is more sensitive to the measure of skewness than to the measure of kurtosis. measures have proved useful (i) in selecting a member of a family such as from the Karl Pearson family, (ii) in developing a test of normality, and (iii) in investigating the robustness of the standard normal theory procedures. The role of the tests of normality in modern statistics has recently been summarized by Shapiro & Wilk (1965). With these applications in mind for the multivariate situations, we propose measures of multivariate skewness and kurtosis. These measures of skewness and kurtosis are developed naturally by extending certain aspects of some robustness studies for the t statistic which involve I1 and 32. It should be noted that measures of multivariate dispersion have been available for quite some time (Wilks, 1932, 1960; Hotelling, 1951). We deal with the measure of skewness in ? 2 and with the measure of kurtosis in ? 3. In ? 4 we give two important applications of these measures, namely, a test of multivariate normality and a study of the effect of nonnormality on the size of the one-sample Hotelling's T2 test. Both of these problems have attracted attention recently. The first problem has been treated by Wagle (1968) and Day (1969) and the second by Arnold (1964), but our approach differs from theirs.

3,774 citations

Journal ArticleDOI
TL;DR: GRADISTAT as discussed by the authors is a computer program for the rapid analysis of grain size statistics from any of the standard measuring techniques, such as sieving and laser granulometry.
Abstract: Grain size analysis is an essential tool for classifying sedimentary environments. The calculation of statistics for many samples can, however, be a laborious process. A computer program called GRADISTAT has been written for the rapid analysis of grain size statistics from any of the standard measuring techniques, such as sieving and laser granulometry. Mean, mode, sorting, skewness and other statistics are calculated arithmetically and geometrically (in metric units) and logarithmically (in phi units) using moment and Folk and Ward graphical methods. Method comparison has allowed Folk and Ward descriptive terms to be assigned to moments statistics. Results indicate that Folk and Ward measures, expressed in metric units, appear to provide the most robust basis for routine comparisons of compositionally variable sediments. The program runs within the Microsoft Excel spreadsheet package and is extremely versatile, accepting standard and non-standard size data, and producing a range of graphical outputs including frequency and ternary plots. Copyright © 2001 John Wiley & Sons, Ltd.

3,419 citations

Journal ArticleDOI
TL;DR: In this article, the authors formalize this intuition with an asset pricing model that incorporates conditional skewness and show that the low expected return momentum portfolios have higher skewnness than high expected return portfolios.
Abstract: If asset returns have systematic skewness, expected returns should include rewards for accepting this risk. We formalize this intuition with an asset pricing model that incorporates conditional skewness. Our results show that conditional skewness helps explain the cross-sectional variation of expected returns across assets and is significant even when factors based on size and book-to-market are included. Systematic skewness is economically important and commands a risk premium, on average, of 3.60 percent per year. Our results suggest that the momentum effect is related to systematic skewness. The low expected return momentum portfolios have higher skewness than high expected return portfolios.

2,628 citations

Journal ArticleDOI
TL;DR: The seasonal Kendall test as discussed by the authors is a nonparametric test for trend applicable to data sets with seasonality, missing values, or values reported as "less than" or values below the limit of detection.
Abstract: Some of the characteristics that complicate the analysis of water quality time series are non-normal distributions, seasonality, flow relatedness, missing values, values below the limit of detection, and serial correlation. Presented here are techniques that are suitable in the face of the complications listed above for the exploratory analysis of monthly water quality data for monotonie trends. The first procedure described is a nonparametric test for trend applicable to data sets with seasonality, missing values, or values reported as ‘less than’: the seasonal Kendall test. Under realistic stochastic processes (exhibiting seasonality, skewness, and serial correlation), it is robust in comparison to parametric alternatives, although neither the seasonal Kendall test nor the alternatives can be considered an exact test in the presence of serial correlation. The second procedure, the seasonal Kendall slope estimator, is an estimator of trend magnitude. It is an unbiased estimator of the slope of a linear trend and has considerably higher precision than a regression estimator where data are highly skewed but somewhat lower precision where the data are normal. The third procedure provides a means for testing for change over time in the relationship between constituent concentration and flow, thus avoiding the problem of identifying trends in water quality that are artifacts of the particular sequence of discharges observed (e.g., drought effects). In this method a flow-adjusted concentration is defined as the residual (actual minus conditional expectation) based on a regression of concentration on some function of discharge. These flow-adjusted concentrations, which may also be seasonal and non-normal, can then be tested for trend by using the seasonal Kendall test.

2,482 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023380
2022846
2021335
2020334
2019279
2018287