Before revision:  It was found that the expected value of excess kurtosis divided by the sample size is finite for any value of the tail index and the sample estimate of kurtosis increase as a linear function of sample size and tail index  .
After revision:  It was found that the expected value of excess kurtosis divided by the sample size is finite for any value of the tail index and the sample estimate of kurtosis increase as a linear function of sample size and tail index . It is very sensitive to changes in the tail-index .