kurtosis is a measure of peakedness of a distribution relative to the normal distribution

Measure of Kurtosis

kurtosis is a measure of peakedness of a distribution relative to the normal distribution. A distribution having a relatively high peak is called leptokurtic. A distribution which is flat topped is called platykurtic. The normal distribution which is neither very peaked nor very flat-topped is also called mesokurtic.  The histogram is an effective graphical technique for showing both the skewness and kurtosis of data set.[Latexpage]

Kurtosis Pict

Data sets with high kurtosis tend to have a distinct peak near the mean, decline rather rapidly, and have heavy tails. Data sets with low kurtosis tend to have a flat top near the mean rather than a sharp peak.

Moment ratio and Percentile Coefficient of kurtosis are used to measure the kurtosis

Moment Coefficient of Kurtosis= $b_2 = \frac{m_4}{S^2} = \frac{m_4}{m^{2}_{2}}$

Percentile Coefficient of Kurtosis = $k=\frac{Q.D}{P_{90}-P_{10}}$
where Q.D = $\frac{1}{2}(Q_3 – Q_1)$ is the semi-interquartile range. For normal distribution this has the value 0.263.

A normal random variable has a kurtosis of 3 irrespective of its mean or standard deviation. If a random variable’s kurtosis is greater than 3, it is said to be Leptokurtic. If its kurtosis is less than 3, it is said to be Platykurtic.

Incoming search terms:

  • percentile coefficient of kurtosis
  • peakedness
  • percentile measure of kurtosis
  • Measures of peakedness in statistics
  • (less Kurtosis or peakedness)
  • heavy tails
  • coefficient of kurtosis
  • skewness kurtosis probability distribution moment-ratio
  • the peakedness of distribution is referred to as
  • peakedness in statistics
Be Sociable, Share!

One Comment

  1. GS says:

    Thanks for update

Leave a Reply

Your email address will not be published. Required fields are marked *


question razz sad evil exclaim smile redface biggrin surprised eek confused cool lol mad twisted rolleyes wink idea arrow neutral cry mrgreen

error: Content is protected !!