Abstract

This presentation is about the use of simulation in investigating and explaining concepts that should form part of 2nd and 3rd level courses in Statistics but are usually omitted. A study of these concepts can be regarded as “course enrichment” and can be helpful in the understanding of some concepts in these courses. The following will be discussed.

1 The sampling distribution of the median that is based on a sample of size n selected from a Cauchy distribution.

It is known that the Central Limit Theorem for the mean does not hold in this case, but this is not the case for the sampling distribution of the median. For which value of n can this distribution be well approximated by the normal distribution?

2 The two-sample permutation test for the equality of means. This test is known to be superior to the t-tests when samples are drawn for non-normal distributions. The robustness of this test will be discussed.

3 Comparison of tests for the equality of variances (F-test, Brown-Forsythe, Fligner-Killeen, Ansari-Bradley tests).

Tests will be compared for samples from Normal, Exponential and Cauchy distributions.

4 Comparing Ordinary Least Squares (OLS) and Least Absoulte Deviations (L1) regressions.

The bias and Mean Square Error for estimating the slope of a straight line are calculated when errors are normal, heavy-tailed (Laplace and t-distributions), skewed or contain outliers.

5 An explanation of the difference between stationarity and ergodicity. Students often find it difficult to distinguish between these concepts. Examples are given of

5.1 A process that is ergodic but not stationary.
5.2 A process that stationary but not ergodic.