CHAPTER 4
Statistical Principles
Beyond the basic ideas of probability theory discussed in Chapter 3, the measurement and the analysis of random data involve uncertainties and estimation errors that must be evaluated by statistical techniques. This chapter reviews and illustrates various statistical ideas that have wide applications to commonly occurring data evaluation problems. The intent is to provide the reader with a minimum background in terminology and certain techniques of engineering statistics that are relevant to discussions in later chapters. More detailed treatments of applied statistics with engineering applications are available from Refs 1–3.
4.1 SAMPLE VALUES AND PARAMETER ESTIMATION
Consider a random variable x, as defined in Section 3.1, where the index k of the sample space is omitted for simplicity in notation. Further consider the two basic parameters of x that specify its central tendency and dispersion, namely the mean value and variance, respectively. From Equations (3.8) and (3.11), the mean value and variance are given by
where p(x) is the probability density function of the variable x. These two parameters of x cannot, of course, be precisely determined in practice because an exact knowledge of the probability density function will not generally ...
