The first four central moments of a distribution are 0, 2.5, 0.7 and 18.75. Test the skewness and Kurtosis of the distribution.

Question: The first four central moments of a distribution are 0, 2.5, 0.7 and 18.75. Test the skewness and Kurtosis of the distribution.

Solution:

Skewness is tested by μ3 which should be equal to zero in a symmetrical distribution. Since in the given problem it is 0.7, we can conclude that the distribution is not symmetrical. But to measure the extent and direction of the skewness we make use of constant.

homework

Since β1 = 3 we conclude that the curve is mesokurtic.