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.

Comments

THE IDEA OF UNIVERSAL BASIC INCOME

In the previous article, we mentioned that Universal Basic Income has been proposed as one of the solutions to the paradox of welfare. Here, we explore what the idea is, its empirical feasibility and the possible hurdles in its implementation. Imagine that one fine morning, you get up and hear the news that the government would now transfer a certain amount of money, every month, in every citizen’s bank account, irrespective of one’s existing employment status, without it getting taxed. This is exactly what the Universal Basic Income would mean! By definition, the UBI is a financial support system that gives a certain minimum amount of money to everybody in the economy, which is needed for the fulfilment of one’s basic needs. However, there exists no consensus on what form this minimum basic income would take, or what amount is necessary for minimum subsistence. Nonetheless, this ambitious social policy is being increasingly viewed as an alternative to the existing system of welfare p

The Paradox of Welfare

Amidst all the possible mechanisms that are used to tackle the problem of poverty, almost everyone would agree on the importance of welfare programmes implemented by governments all over the world. These programmes take the form of subsidies provided by the government for necessities like housing, food, energy and healthcare. But critiques of these poverty alleviation programmes have pointed out the ironic effect they have on people struck in poverty. This phenomenon is known as the ‘welfare trap’. Here’s how it works. The governmental assistance is provided to people who are unable to find work and whose income falls below a particular level. The benefits are then phased out when they enter the job market and their income crosses the threshold level. Now, since people in poverty are also rational actors, they are disincentivised from taking up work even when they are able to, when they realise that there is no net benefit that they gain from working. This happens since the jobs t

The Debate on Economic Sanctions

Since the last century, the era of military wars appears to have come to an end, leading the global community on a quest to find alternative ways of conflict resolution and protecting international law. One of these ways is imposing economic sanctions on other countries. These are restrictions or outright ban on trade, currency flows or investments from the other country. But do economic sanctions achieve their objective? History tells us that arguably, the answer to this question is that they don't. Formerly imposed sanctions on countries like Iraq, Iran, North Korea and recently, Russia, indicate that these sanctions not only turn out to be inefficient in barring the sanctioned countries from violating international peace, but also prove detrimental to other countries who are dependent on the sanctioned countries for necessities like food supplies, oil, etc. For instance, the recent imposition of economic sanctions on Russia by the US in the light of the Ukrainian war caused th

Off The Z Table

Search This Blog