Dictionary

This page serves as a dictionary of terms which I tend to use that might be (a)unfamiliar to folks; or, (b) be sufficiently obscure; or, (c) borrowed in a specific context from another.

Gaussian Distribution: is a type of continuous probability distribution for a real-valued random variable.

The parameter μ is the mean or expectation of the distribution (and also its median and mode); and σ is its standard deviation. The variance of the distribution is σ^2. A random variable with a Gaussian distribution is assumed to be normally distributed and is called a normal deviate.

Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. Their importance is partly due to the central limit theorem. It states that, under some conditions, the average of many samples (observations) of a random variable with finite mean and variance is itself a random variable whose distribution converges to a normal distribution as the number of samples increases.

Therefore, physical quantities that are expected to be the sum of many independent processes (such as measurement errors) often have distributions that are nearly normal. Many many errors are made by people trying to predict the future through the extrapolation of past behavior using Gaussian distributions.

Inductive Reasoning: is a method of reasoning in which the premises are viewed as supplying some evidence for the truth of the conclusion; this is in contrast to deductive reasoning. While the conclusion of a deductive argument is certain, the truth of the conclusion of an inductive argument may be probable, based upon the evidence given.

From Nassim Nicholas Taleb’s Incerto book series

  • Mediocristan is where one must endure the tyranny of the collective, the routine, the obvious, and the predicted. Matters that seem to belong to Mediocristan (subjected to what Taleb calls type 1 randomness): height, weight, calorie consumption, income for a baker, a small restaurant owner, a prostitute, or an orthodontist; gambling profits (in the very special case, assuming the person goes to a casino and maintains a constant betting size), car accidents, mortality rates, “IQ” (as measured).
  • Extremistan is where one is subjected to the tyranny of the singular, the accidental, the unseen, and the unpredicted. Matters that seem to belong to Extremistan (subjected to what Taleb calls type 2 randomness): wealth, income, book sales per author, book citations per author, name recognition as a “celebrity,” number of references on Google, populations of cities, uses of words in a vocabulary, numbers of speakers per language, damage caused by earthquakes, deaths in war, deaths from terrorist incidents, sizes of planets, sizes of companies, stock ownership, height between species (consider elephants and mice), financial markets (but your investment manager does not know it), commodity prices, inflation rates, economic data.