CHAPTER
10
Using Data The last two chapters described methods for constructing probability distributions, which, of course, is what we use to model uncertainties in our decision problems. Chapter 8 used subjective assessments for the source of the probabilities, and Chapter 9 introduced theoretical distributions. We now discuss a variety of ways to construct probability distributions using data. First, we show how data can be used either to select a theoretical distribution or to build an empirical distribution (a distribution based only on observations). Second, we use data to model relationships, and then use these relationships to build more precise distributions. For example, data can help determine the relationship between a company’s profit and its sales force size, thereby helping to predict future profits more precisely. Although we touch upon many topics in Chapter 10, the focus is always on building useful probability models for the uncertainties in our decision problem.
USING DATA TO CONSTRUCT PROBABILITY DISTRIBUTIONS In this section, we show how historical data can be used in two different ways to construct probability distributions. Either we can directly construct a distribution based solely on the data or we can use the data to select a theoretical distribution that fits the data. Both of these methods are conceptually straightforward, but can be computationally intensive. Luckily for us, @RISK will do all the computations. The @RISK instructions appear at the end of this section rather than at the end of the chapter. Data for decision models come in essentially two forms: sample data, which are observations of the uncertain quantity, or subjectively assessed data. Sample data are usually of the form of n observations and denoted x1, x2, …, xn , where each xi is a known number. For example, if we were interested in a particular stock’s performance, we might gather a sample of the stock’s monthly returns: 1.2%, 0.8%, …, 0.3%. In contrast, subjectively 418 Copyright 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.