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Kurtosis: The extent to which the peak of the unimodal probability distribution or the frequency distribution departs from its shape of the normal distribution, by either being more pointed (like leptokurtic)or flatter ( like platykurtic). Commonly measured for a probability distribution as
where 4 is the fourth central moment of distribution, and 2 is its variance.
(consequent functions of sample moments are used for frequency distributions.)
For the normal distribution this index takes the value three and often index is redefined as the value above minus three so that the normal distribution would contain the value zero.
(Other distributions with the zero kurtosis are known as mesokurtic.) For the distribution which is leptokurtic the index is positive and for the platykurtic curves it is negative. It is shown in the figure
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Bimodal distribution : The probability distribution, or we can simply say the frequency distribution, with two modes. Figure 15 shows the example of each of them
Cauchy distribution : The probability distribution, f (x), can be given as follows where α is the position of the parameter (median) and the beta β a scale parameter. Moments
stationary time series
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