Overview

The reader is urged to pay special attention to this Chapter. Here the basic concepts familiar to a novice as well as to a seasoned researcher are used in a somewhat non-orthodox manner. The results are practically useful. Also, new avenues for further research are available here in great abundance.

In this chapter we discuss construction of confidence intervals for R= P(X as well as testing hypotheses concerning R when distributions of variables X and Y have known forms with one or several unknown parameters (the so-called parametric inference). The extensive literature on interval estimation in the case when the distributions of X and Y are unspecified (the nonparametric inference) will be covered in Chapter 5.

As it follows from Section 2.4, there are three groups of methods for construction of confidence intervals applicable to our problem: exact, asymptotic and Bayesian methods. We shall study each of them in turn concluding the section with a discussion of hypotheses testing and bootstrap techniques.

4.1 Confidence Intervals Based on Exact Distributions

In Section 2.4, exact confidence interval for R in the case of the one-parameter exponential distribution has been derived. Historically, however, the first exact confidence intervals have been obtained in the case of the normal distribution. We draw reader's attention to the fact that although construction of the exact confidence intervals usually requires cumbersome and occasionally sophisticated calculations, these intervals are by far more reliable than the asymptotic ones, especially, in...