Kurtosis Measures Bimodality?

Hildebrand, David K.

doi:10.1080/00031305.1971.10477241

Cited by 21 publications

(13 citation statements)

References 6 publications

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“…In the wave saturation regime, a redistribution of probability mass into the PDF shoulders is observed. Examples found in Hildebrand (1971) and DeCarlo (1997) for the symmetric Beta distribution illustrates a similar aspect. Note that in Fig.…”

Section: Statistical Moments and Comparison With Literature Datasupporting

confidence: 53%

“…DeCarlo (1997) pointed out that a strong negative excess kurtosis might also be used as indicator of PDF bi-modality DeCarlo (1997). However, as pointed out by Hildebrand (1971), although this interpretation may be true, there are counter examples (such as the family of double-Gamma distributions) which oppose this view. A more general interpretation for symmetric distributions could be that a movement of probability mass from or into the shoulders of a distribution into or from its centre or tails implies in changes of its kurtosis.…”

Section: Statistical Momentsmentioning

confidence: 97%

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Statistical characterization of interfacial waves in turbulent stratified gas-liquid pipe flows

Ayati

Carneiro

2018

International Journal of Multiphase Flow

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This study presents a statistical analysis of interfacial waves in a turbulent stratified air-water flow inside a 10 cm diameter pipe. Wave elevation measurements were acquired using conductance probes with high sampling rate, Sr = 500Hz. Local wave parameters (elevation, crest height, trough height, etc.) were extracted using a zero-crossing technique. The evolution of their corresponding statistical distributions and statistical moments was investigated for varying flow conditions.The main goal of this study is to offer an alternative method for distinguishing between various wavy flow patterns. The proposed approach is based on the Gaussian model, which is widely used in the characterization of ocean waves. Instead of the traditional sub-regime categorization which is based on a combination of visual observations and qualitative spectral description, this method categorizes a wave field depending on its degree of non-linearity and statistics of elevation parameters. This approach also allows parametrization of the interfacial structure. As a first step, this approach was carried out only for a selected set of flow rate combinations, in which the liquid superficial velocity was kept constant at U sl = 0.10 m/s whilst the superficial velocity was increased from 1.0 m/s to 4.0 m/s with increments of 0.25 m/s. Subsequently, statistical moments of the interface elevation were computed and compared to literature data, for varying U sl and U sg . Based on the detailed statistical description of wave data, two flow regimes are categorized: wave amplitude growth and saturation. These regimes were also identified as quasi-Gaussian and non-Gaussian, respec-Email addresses: awalaa@math.uio.no (A.A. Ayati),

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Section: Statistical Moments and Comparison With Literature Datasupporting

confidence: 53%

Section: Statistical Momentsmentioning

confidence: 97%

Statistical characterization of interfacial waves in turbulent stratified gas-liquid pipe flows

Ayati

Carneiro

2018

International Journal of Multiphase Flow

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“…Thus, we first transformed the distribution of times to invasion by means of a Box-Cox transformation, which makes the distribution as symmetrical as possible. Significant negative kurtosis in a symmetric distribution means that the shoulders of the distribution are higher than they would be in a normal distribution, and a value beyond (1.2 means significant bimodality (Hildebrand 1971, Wyszomirski 1992. After Box-Cox transformation we found significant negative kurtosis in the distribution of times to invasion (kurtosis0(0.98, SE 00.4, p00.007).…”

Section: Statistical Analysesmentioning

confidence: 78%

Using survival regression to study patterns of expansion of invasive species: will the common waxbill expand with global warming?

Reino¹,

Moya-Laraño²,

Heitor³

2009

Ecography

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Different approaches can be used to model the spread of invasive species. Here we demonstrate the use of survival regression, an approach that can be used to study a variety of events, not just death, to model the time to colonization. The advantage of survival regression to study colonisation of new areas is that information on those areas that have not been invaded by the end of a study can be included in the analysis, thus potentially increasing the accuracy of parameter estimation. We use proportional hazards regression (PHR; a type of survival regression) to model the spread of the common waxbill Estrilda astrild in Portugal. The species invaded Portugal in two peaks of invasion between 1964 and 1999. We built a PHR model with the information available up to the first invasion peak, then used this model to predict the pattern of invasion in the second peak. PHR had useful forecasting capabilities: areas that were actually colonised by 1999 had significantly higher hazards of colonization based on information from the first wave of invasion than areas that were not colonised. We then built a final model of expansion of the common waxbill that combined all available data up to 1999. Among climate variables, the most important predictor of colonization was temperature, followed by relative humidity. We used this model to estimate the invasion potential of the species under climate change scenarios, observing that an increase of 18C in mean annual temperature increased the risk of a new invasion by 47%. Our analyses suggest that survival regression may be a useful tool for studying the geographical spread of invasive species. However, PHR was conceived as a descriptive technique rather than as a predictive tool, and thus further research is needed to empirically test the predictive capabilities of PHR.

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“…Similarly, the kurtosis indicates the degree of modality versus bimodality, although its meaning is somewhat ambiguous. The traditional interpretation of kurtosis as a measure of "peakedness" has largely shifted among statisticians toward a focus on bimodality, although a stream of research has suggested that the meaning of kurtosis is complex and necessitates caution in its interpretation (Balanda and MacGillivray, 1988;Chissom, 1970;Darlington, 1970;DeCarlo, 1997;Hildebrand, 1971;Moors, 1986;Ruppert, 1987)-a perspective with which we fully concur. By measuring modality versus bimodality, the kurtosis quantifies the extent to which respondents are clustered into two extreme camps, making it an intuitively appealing way to gauge group polarization.…”

Section: Polarization Bimodality and Kurtosismentioning

confidence: 91%

Attitudinal Polarization and Trimodal Distributions: Measurement Problems and Theoretical Implications

Downey

Huffman

2001

Social Science Quarterly

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Objective. We present trimodality as a distributional pattern that is relevant to conceptual issues of attitudinal polarization but fits nowhere along the modalitybimodality continuum. Methods. We use simulated univariate distributions and distributions taken from the 1994 General Social Survey to investigate how commonly used measures track (or fail to track) noteworthy shifts in the distributions. Results. The kurtosis and variance are largely insensitive to important distributional differences, most importantly that between bimodality and trimodality. Conclusions. We argue that the lack of attention to trimodality and the insensitivity of commonly used measures of polarization (kurtosis in particular) to that distributional pattern create a blind spot in our thinking about polarization and can lead to basic misinterpretations of extant patterns in public opinion data.Social polarization occupies an important place in theories of democracy because of its inverse relation to social consensus. Recently, it has become the focal point of debates surrounding contemporary social conflicts known collectively as the "culture wars." The use of attitudinal research to assess claims underlying the culture wars thesis has sparked methodological developments and debates concerning the measurement of attitudinal polarization and has made it an important topic for public opinion research. In that research, polarization is conceptualized as the extent to which attitudes either cluster around a central mode or are divided between two disparate positions. Polarization, then, is assumed to exist along a continuum from modality to bimodality.

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Kurtosis Measures Bimodality?

Cited by 21 publications

References 6 publications

Statistical characterization of interfacial waves in turbulent stratified gas-liquid pipe flows

Statistical characterization of interfacial waves in turbulent stratified gas-liquid pipe flows

Using survival regression to study patterns of expansion of invasive species: will the common waxbill expand with global warming?

Attitudinal Polarization and Trimodal Distributions: Measurement Problems and Theoretical Implications

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