Kurtosis Formula. For a sample of n values a method of moments estimator of the population excess kurtosis can be defined as where m 4 is the fourth sample moment about the mean m 2 is the second sample moment about the mean that is the sample variance x i is the i th value and is the sample mean. For a very large sample very high n the differences between and among n 1 n n 1 n 2 and n 3 are becoming negligible and the sample kurtosis formula approximately equals.
Mathematically it is represented as kurtosis n σni yi y 4 σni yi y 2 2. 1987 1987 1991 1992 1992 1992 1992 1993 1994 1994 1995. For a very large sample very high n the differences between and among n 1 n n 1 n 2 and n 3 are becoming negligible and the sample kurtosis formula approximately equals.
For a sample of n values a method of moments estimator of the population excess kurtosis can be defined as where m 4 is the fourth sample moment about the mean m 2 is the second sample moment about the mean that is the sample variance x i is the i th value and is the sample mean.
One can reparameterize with m 5 2 3 γ2 displaystyle m 5 2 3 gamma 2 where γ2 displaystyle gamma 2 is the kurtosis as defined above. The formula for kurtosis in excel involves the sample size sample standard deviation and the sample mean. The greater the value of beta 2 the more peaked or leptokurtic the curve. Proc means data test kurtosis vardef n.
