Elliot A. Tanis

An Iterated Procedure for Testing the Equality of Several Exponential Distributions

Abstract This iterated procedure is used to test the equality of the scale and location parameters of several independent exponential distributions. In essence, these applications of this procedure consist of repeated use of certain two-sample statistics which were considered by Epstein and Tsao. A rejection by this iterated scheme provides some reason why all the distributions are not equal. In addition, under the null and alternative hypotheses, certain of these test statistics are independent. This means that it is very easy to compute the power at certain alternative hypotheses as well as the significance level of the procedure. A few comparisons are made with some over-all tests which are essentially due to Sukhatme.

Mathematical Probability and Statistics Computer Laboratory.

Summary Some concepts in probability and statistics can be illustrated with random experiments which use dice, cards, and urns containing colored beads. However the nature of such experiments limits their applicability and often dictates that sample sizes must be small. The computer allows us to efficiently simulate many different types of random experiments. In order for a student to write a computer program which will simulate a physical experiment, he is required to understand the experiment and available simulation techniques. It is also possible for a student to simulate theoretical results and in so doing he gains a better understanding and appreciation of the theory. Laboratory exercises have been written for a year‐long course in mathematical probability and statistics. Some of the exercises illustrate the simulation of physical experiments, while others help the student understand theoretical concepts. The students are encouraged to experiment. For example, if certain hypotheses in a theorem are ...