Univariate Probability Models—Continuous

Abstract

Among the continuous univariate probability models, the ones most commonly used are the Normal or Gaussian distribution, the Exponential distribution, the Gamma distribution and the Rectangular distribution. A list of the commonly used univariate continuous probability models is given in Table 6.1. Among these models, the Normal distribution is the most important one. There are several reasons for its importance. A good many types of data, when represented by frequency curves, the curves approximate to the Normal curve. There are also theoretical justifications for its importance. One is stated in a theorem called the Central Limit Theorem, which is given in the next chapter. It states that a certain function of the sample values has a Normal distribution when the sample size is large, whatever be the parent distribution. There are also a number of characteristic properties of the Normal distribution. That is, properties such as the statistical independence of the sample mean and the sample variance will uniquely determine the Normal distribution. In this chapter we will discuss the Normal distribution in detail and briefly mention the other distributions. Additional material is given in the problems at the end of the chapter.