On normal distribution

Since its introduction, the normal distribution has been known by many different names: the law of error, the law of facility of errors, Laplace’s second law, Gaussian law, etc. Gauss himself apparently coined the term with reference to the “normal equations” involved in its applications, with normal having its technical meaning of orthogonal rather than “usual”. However, by the end of the 19th century some authors had started using the name normal distribution, where the word “normal” was used as an adjective — the term now being seen as a reflection of the fact that this distribution was seen as typical, common – and thus “normal”.

Peirce (one of those authors) once defined “normal” thus: “…the ‘normal’ is not the average (or any other kind of mean) of what actually occurs, but of what would, in the long run, occur under certain circumstances.”

Around the turn of the 20th century Pearson popularized the term normal as a designation for this distribution:

“Many years ago I called the Laplace­ Gaussian curve the normal curve, which name, while it avoids an international question of priority, has the disadvantage of leading people to believe that all other distributions of frequency are in one sense or another ‘abnormal’. — Pearson (1920) ”

The term “standard normal” which denotes the normal distribution with zero mean and unit variance came into general use around 1950′s, appearing in the popular textbooks by P.G. Hoel (1947) “Introduction to mathematical statistics” and A.M. Mood (1950) “Introduction to the theory of statistics”.

When the name is used, the “Gaussian distribution” was named after Carl Friedrich Gauss, who introduced the distribution in 1809 as a way of rationalizing the method of least squares. The related work of Laplace, also outlined above, has led to the normal distribution being sometimes called Laplacian, especially in French-speaking countries. Among English speakers, both “normal distribution” and “Gaussian distribution” are in common use, with different terms preferred by different communities.

Submitted by Dulal Bhaumik, University of Illinois at Chicago