Sample Kurtosis Formula. Sample kurtosis definitions a natural but biased estimator. This formula uses the unbiased estimates of variance and of the fourth moment about the mean.
Definition of kurtosis for univariate data y1 y2 yn the formula for kurtosis is. This formula uses the unbiased estimates of variance and of the fourth moment about the mean. S sample standard deviation.
The third formula below can be found in sheskin 2000 and is used by spss and sas proc means when specifying the option vardef df or by default if the vardef option is omitted.
The formula for kurtosis is expressed as the ratio of the fourth moment and variance s 2 squared or squared the second moment of the distribution. Sample kurtosis definitions a natural but biased estimator. 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. Therefore we are always interested in the excess kurtosis i e excess kurtosis sample kurtosis 3 where.
