The skewness and peakedness indices, g 1 and g2

Pierre Jolicoeur
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Pierre Jolicoeur: University of Montreal, Department of Biological Science

Chapter Chapter 13 in Introduction to Biometry, 1999, pp 82-88 from Springer

Abstract: Abstract The probability distribution of a continuous variate is usually assumed to be normal in a majority of statistical methods. Theskewnessandpeakednessindices,g 1 ,andg 2 may be used to test that normality assumption. While the agreement between the frequency distribution of a set of data and a theoretical distribution (such as the normal distribution) can also be checked through tests of goodness of fit (chapter 16), the latter require a large sample (containing preferably 100 or more observations). Theg 1 , and g 2 indices can be used even in the case of a small sample and also have the advantage of providing explicit answers concerning the skewness(also calledasymmetry)and thepeakedness(also calledkurtosis)of an observed distribution (Figure 13.2.1 and Figure 13.2.2).Peaked distributions generally have longer tails than flat distributions, but peakedness is a complex property which cannot be reduced to dispersion (section 4.5) and cannot be measured like the latter simply by the variance or the standard deviation.

Keywords: Geometrical Meaning; Fourth Moment; Acceptance Region; Sample Moment; Longe Tail (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1007/978-1-4615-4777-8_14

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