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Uses, limitations and abuses of the ‘Normal’ Distribution

Early researchers on probability distributions thought they had found a model that could be applied to a wide range of situations in nature and society. They called it the Normal Distribution. The model also had nice mathematical properties which made it useful as a basis for many statistical techniques. Its use became widespread.

But there is actually nothing 'normal' about the Gaussian distribution. The universality of its application has been exaggerated especailly in social science. We will consider how it came to occupy such a position and some of the problems this has led to. We will also look in particular at how the misapplication of probabilistic models based on it were a cause of the ccurrent financial crisis. The normal distribution is misnamed: it is not normal when applied to financial data or asset prices.

We will also consider the importance of the fundamental distinction between uncertainty and risk, and alternative models based on power laws.

Illustrative Reading:

Mandelbrot, Benoit B and Richard L. Hudson, The (mis)Behaviour of Markets: A Fractal View of Risk, Ruin and Reward, Profile Books, 2008.

Taleb, Nassim: Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets, Penguin, 2004. Also, The Black Swan: The Impact of the Highly Improbable, Penguin, 2007.

Haldane, Andrew and Benjamin Nelson, “Tails of the unexpected,” Financial Stability, Bank of England, June 2012, downloadable from http://www.bankofengland.co.uk/publications/Documents/speeches/2012/speech582.pdf.