Let x1…, xn be a sample from a distribution with infinite expectation, then for n→∞ the sample average Xn tends to +∞ with probability 1 (see ). Sometimes Xn contains high jumps due to large observations. In this paper we consider samples from the "absolute Cauchy" distribution. In practice, on may consider the logarithm of the observations as a sample from a normal distribution. So we found in our simulation. After rejecting the log-normality assumption, one will be tempted to regard the extreme observations as outliers. It is shown that the discarding of the outlying observations gives an underestimation of the expectation, variance and 99 percentile of the actual distribution.
|Publication status||Published - 1968|