Kurtosis Normality Measure, Introduction, Interpretation

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.

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:

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Your email address will not be published.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 !!