# Normal Distribution

• Anirban DasGupta
Chapter
Part of the Springer Texts in Statistics book series (STS)

## Abstract

Empirical data on many types of variables across disciplines tend to exhibit unimodality and only a small amount of skewness. It is quite common to use a normal distribution as a model for such data. The normal distribution occupies the central place among all distributions in probability and statistics. When a new methodology is presented, it is usually first tested on the normal distribution. The most well-known procedures in the toolbox of a statistician have their exact inferential optimality properties when sample values come from a normal distribution. There is also the central limit theorem, which says that the sum of many small independent quantities approximately follows a normal distribution. Theoreticians sometimes think that empirical data are often approximately normal, while empiricists think that theory shows that many types of variables are approximately normally distributed. By a combination of reputation, convenience, mathematical justification, empirical experience, and habit, the normal distribution has become the most ubiquitous of all distributions. It is also the most studied; we know more theoretical properties of the normal distribution than of others. It satisfies intriguing and elegant characterizing properties not satisfied by any other distribution. Because of its clearly unique position and its continuing importance in every emerging problem, we discuss the normal distribution exclusively in this chapter.

## Keywords

Lognormal Distribution Standard Normal Distribution Standard Normal Variable Mills Ratio General Normal Distribution
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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