fourth moment about mean
square of the second moment
PDFs with values of K less than 3 are called platykurtic (fat or short-tailed), and those with values greater than 3 are called leptokurtic (slim or long-tailed). See Figure A.3. A PDF with a kurtosis value of 3 is known as mesokurtic, of which the normal distribution is the prime example. (See the discussion of the normal distribution in Section A.6.)
We will show shortly how the measures of skewness and kurtosis can be combined to determine whether a random variable follows a normal
distribution. Recall that our hypothesis-testing procedure, as in the t and F tests, is based on the assumption (at least in small or finite samples) that the underlying distribution of the variable (or sample statistic) is normal. It is therefore very important to find out in concrete applications whether this assumption is fulfilled.
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