Outline of a Theory of Powerful Selection of Distribution Functions

摘要

The conventional method of analyzing a given set of test data consists in assuming a distribution function and estimating its parameters. The only way of deciding whether the function is acceptable or not and which of two assumed functions is the better one is by means of a test of goodness-of-fit. For small and moderate sample sizes this test makes a very unreliable basis for a decision, and the confidence that can be put in the choice is practically unknown. In order to eliminate these deficiencies a new method, called the method of powerful selection, is proposed. By use of a test statistic, called the selector, it is possible, without preceding parameter estimations, to state the acceptability of a function on the basis of a preassigned level-of-significance and the decision power, that is, the chance of making a true decision between two functions. The tools of this method are presented and their applications illustrated by numerical analyses of some fatigue-test series. It will not too seldom occur that none of several assumed functions will be accepted. In this situation the selectors can be used for diagnosing the rejected functions with regard to causes such as outlying observations, composed populations, and contaminated data. (Author)