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The Not-So-Normal Story of Normality

Being students of economics, we have been made to study the Z table excessively throughout our statistics journey. Hence, before going off the Z table, we decided to explore more about the Z table itself. 


In other words, having learned its technical use in solving a wide variety of statistical problems, we now delve into the interesting history of the normal distribution, unarguably the most popular distribution in modern statistics. The distinctive characteristics of symmetricity and bell-shaped structure impart normality a wide range of real-life applications in physics, biology, finance, hydrology, etc.


Abraham DeMoivre

Interestingly, the major credit for the origin of the normal distribution, also called the Gaussian distribution, does not go to Carl Gauss, but rather to Abraham de Moivre,  a mathematician and a contemporary of Isaac Newton. He used to plot the results of multiple binomial distribution simulations. Consequently, he discovered a pattern that resembled a bell shape. The discovery led to the journey which finally brought us to the Central Limit Theorem, which emphasized the theoretical importance of the normal distribution. More and more data sets were plotted, and every time a bell-shaped curve was observed. Thus, it became 'normal' to expect the 'normal' curve and soon, normality became an assumption for a bunch of data sets. Though, when this term was coined by Gauss, its meaning was orthogonal rather than the commonly implied meaning today.


However, to add an interesting twist to the story, mathematician Benoit Mandelbrot argued that financial prices were not normally distributed. But normality had become a popular assumption in the world of finance, arguably leading to underestimation of risk. And then in 2008, the world saw the Great Recession. 


Was there a causal relation that vindicated mathematicians like Mandelbrot? Certainly, there is a vast pool of information to discover out there.

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