This is just an Excerpt from a larger document, click here to view the entire document.Introduction
This START sheet discusses some empirical and practical methods for checking and verifying the statistical assumptions of an Exponential distribution and presents several numerical and graphical examples showing how these methods are used. Most statistical methods (of parametric statistics) assume an underlying distribution in deriving results (methods that do not assume an underlying distribution are called non-parametric, or distribution free, and will be the topic of a separate paper).
Whenever we assume that the data follow a specific distribution we also assume risk. If the assumption is invalid, then the confidence levels of the confidence intervals (or the hypotheses tests) will be incorrect. The consequences of assuming the wrong distribution may prove very costly. The way to deal with this problem is to check distribution assumptions carefully, using the practical methods discussed in this paper.
There are two approaches to checking distribution assumptions. One is to use the Goodness of Fit (GoF) tests. These are numerically convoluted, theoretical tests such as the Chi Square, Anderson-Darling, Kolmogorov-Smirnov, etc. They are all based on complex statistical theory and usually require lengthy calculations. In turn, these calculations ultimately require the use of specialized software, not always readily available. Alternatively, there are many practical procedures, easy to understand and implement. They are based on intuitive and graphical properties of the distribution that we wish to assess and can thus be used to check and validate these distribution assumptions. The implementation and interpretation of such procedures, for the important case of the Exponential distribution, so prevalent in quality and reliability theory and practice, are discussed in this paper.
Also addressed in this START sheet are some problems associated with checking the Exponential distribution assumption. First, a numerical example is given to illustrate the seriousness of this problem. Then, additional numerical and graphical examples are developed that illustrate how to implement such distribution checks and related problems.