Steekproeven uit de halve cauchy verdeling

Summary Let x₁…, x_n be a sample from a distribution with infinite expectation, then for n→∞ the sample average x?_n tends to +∞ with probability 1 (see [4]). Sometimes x?_n 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.