Now suppose someone tells you that they have calculated positive excess kurtosis from either data or a pdf.
#Name 3 measures of dispersio pdf#
We could also say, based on the 0.5*N(0, 1) + 0.5*N(4,1) distribution, that negative excess kurtosis implies that the pdf is “wavy.” It’s like saying, “well, I know all bears are mammals, so it must be the case that all mammals are bears.” If that were so, we could say, based on the beta(.5,1) distribution, that negative excess kurtosis implies that the pdf is infinitely pointy. But obviously, a single example does not prove the general case. Yes, the U(0,1) distribution is flat-topped and has negative excess kurtosis. These are just two examples out of an infinite number of other non-flat-topped distributions having negative excess kurtosis. For another example, the 0.5*N(0, 1) + 0.5*N(4,1) distribution is bimodal (wavy) not flat at all, and also has negative excess kurtosis similar to that of the uniform (U(0,1)) distribution. For one example, the beta(.5,1) has an infinite peak and has negative excess kurtosis. According to the “peakedness” dogma (started unfortunately by Pearson in 1905), you are supposed to conclude that the distribution is “flat-topped” when graphed. Suppose someone tells you that they have calculated negative excess kurtosis either from data or from a probability distribution function (pdf). Here is why “peakedness” is wrong as a descriptor of kurtosis. The accuracy of the variance as an estimate of the population $\sigma^2$ depends heavily on kurtosis.Kurtosis helps in determining whether resource used within an ecological guild is truly neutral or which it differs among species.In finance, risk and insurance are examples of needing to focus on the tail of the distribution and not assuming normality.
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If its kurtosis is less than 3, it is said to be Platykurtic.Ī large value of kurtosis indicates a more serious outlier issue and hence may lead the researcher to choose alternative statistical methods. If a random variable’s kurtosis is greater than 3, it is said to be Leptokurtic. So, kurtosis is all about the tails of the distribution – not the peakedness or flatness.Ī normal random variable has a kurtosis of 3 irrespective of its mean or standard deviation. The kurtosis parameter is a measure of the combined weight of the tails relative to the rest of the distribution. For normal distribution this has the value 0.263. Moment Coefficient of Kurtosis= $b_2 = \frac(Q_3 – Q_1)$ is the semi-interquartile range.