Normal.pdf. History of normal distribution and how its extensive usage made economics/finance abnormal.. Andy Haldane once again.
I mean how he keeps coming up with one terrific speech after the other. In his latest speech/paper Haldane looks at the history if normal distribution. He goes into historical details of how the distribution came up, how and why it was given the name normal, how it moved from sciences to social sciences and finally into economics. And he links all this in a typical Haldane style connecting finance/economics to many things in nature. Just like other papers this one is so good that it is difficult to summarise the thoughts. Infact, there is very little in economics and finance that resembles normal distribution with thin tails. For almost a century, the world of economics and finance has been dominated by randomness.
But as Nassim Taleb reminded us, it is possible to be Fooled by Randomness (Taleb (2001)). The normal distribution provides a beguilingly simple description of the world. He points to this fascinating tale where Sotheby’s was fooled into randomness: Non-Normal Distributions in the Real World. By Thomas Pyzdek Introduction One day, early in my career in quality, I was approached by Wayne, a friend and the manager of the galvanizing plant.
"Tom" he began, "I have really been pushing quality in my area lately and everyone is involved. One of the areas we are working on is the problem of plating thickness. Your reports always show 3% - 7% rejects and we want to drive that number down to zero. " I was, of course, pleased. Normal Distribution. History The normal curve was developed mathematically in 1733 by DeMoivre as an approximation to the binomial distribution.
His paper was not discovered until 1924 by Karl Pearson. Non-Normal Distributions in the Real World. Stahl96.pdf. History of Normal Distribution. History of the Normal Distribution Author(s) David M.
Lane Prerequisites Distributions, Central Tendency, Variability, Binomial Distribution In the chapter on probability, we saw that the binomial distribution could be used to solve problems such as "If a fair coin is flipped 100 times, what is the probability of getting 60 or more heads? " where x is the number of heads (60), N is the number of flips (100), and π is the probability of a head (0.5). Abraham de Moivre, an 18th century statistician and consultant to gamblers, was often called upon to make these lengthy computations. de Moivre noted that when the number of events (coin flips) increased, the shape of the binomial distribution approached a very smooth curve. Figure 1. De Moivre reasoned that if he could find a mathematical expression for this curve, he would be able to solve problems such as finding the probability of 60 or more heads out of 100 coin flips much more easily.
Figure 2. BBC Radio 4 - A Brief History of Mathematics, Carl Friedrich Gauss. Gauss - 19th Century Mathematics. Carl Friedrich Gauss is sometimes referred to as the "Prince of Mathematicians" and the "greatest mathematician since antiquity".
He has had a remarkable influence in many fields of mathematics and science and is ranked as one of history's most influential mathematicians. Gauss was a child prodigy. There are many anecdotes concerning his precocity as a child, and he made his first ground-breaking mathematical discoveries while still a teenager. At just three years old, he corrected an error in his father payroll calculations, and he was looking after his father’s accounts on a regular basis by the age of 5. At the age of 7, he is reported to have amazed his teachers by summing the integers from 1 to 100 almost instantly (having quickly spotted that the sum was actually 50 pairs of numbers, with each pair summing to 101, total 5,050). Gauss gave the first clear exposition of complex numbers and of the investigation of functions of complex variables in the early 19th Century.
Cc07s.pdf. Generalizedgamma.pdf. Introduction to Normal Distributions. Introduction to Normal Distributions Author(s) David M.
Lane Prerequisites Distributions, Central Tendency, Variability Learning Objectives. Areas under Normal Distribution. Areas Under Normal Distributions Author(s) David M.
Lane Prerequisites Distributions, Central Tendency, Variability, Introduction to Normal Distributions Learning Objectives State the proportion of a normal distribution within 1 and within 2 standard deviations of the mean Use the calculator "Calculate Area for a given X" Use the calculator "Calculate X for a given Area" Areas under portions of a normal distribution can be computed by using calculus.
Figure 1. Standard Normal Distribution. Normal Distribution. A normal distribution is a very important statistical data distribution pattern occurring in many natural phenomena, such as height, blood pressure, lengths of objects produced by machines, etc.
Certain data, when graphed as a histogram (data on the horizontal axis, amount of data on the vertical axis), creates a bell-shaped curve known as a normal curve, or normal distribution. Normal distributions are symmetrical with a single central peak at the mean (average) of the data.