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Fat Tails
"... You’ve probably heard of Lake Wobegon, the little town in Minnesota where all the children are above average. There’s been much head-scratching about this statistical miracle. What happens to the kids who fail to surpass themselves? Are they shipped across the lake to another little town, where all ..."
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You’ve probably heard of Lake Wobegon, the little town in Minnesota where all the children are above average. There’s been much head-scratching about this statistical miracle. What happens to the kids who fail to surpass themselves? Are they shipped across the lake to another little town, where all the children are below average? That practice wouldn’t necessarily work to the detriment of either community. It might be like the migration from Oklahoma to California during the Dust Bowl years, which Will Rogers said raised the average intelligence of both states. One small town that beats the law of averages is strange enough, but even more mystifying is the finding that Lake Wobegon is not unique— that in fact everyone is above average. In 1987 John J. Cannell, a West Virginia physician and activist, discovered that all 50 states report that their children do better than the national average on standardized tests. (And this was years before the No Child Left Behind Act!) I can’t promise to resolve these paradoxes. On the contrary, I’m going to make matters worse by describing still more funny business in the world of averages. The story that follows is about a data distribution that simply has no average. Given any finite sample drawn from the distribution, you are welcome to apply the usual algorithm for the arithmetic mean—add up the values and divide by the size of the sample— but the result won’t mean much. Whatever average you calculate in this way, you can improve it just by taking a bigger sample. Perhaps this is the secret of the Lake Wobegon school board.
fat-tailed
, 2015
"... The effect of breed on fatty acid composition of subcutaneous adipose tissues in ..."
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The effect of breed on fatty acid composition of subcutaneous adipose tissues in
The Origin of Fat Tails
"... We propose a random walk model of asset returns where the parameters depend on market stress. Stress is measured by, e.g., the value of an implied volatility index. We show that model parameters including standard deviations and correlations can be estimated robustly and that all distributions are a ..."
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are approximately normal. Fat tails in observed distributions occur because time series sample different stress levels and therefore different normal distributions. This provides a quantitative description of the observed distribution including the fat tails. We discuss simple applications in risk management
On Bayesian modeling of fat tails and skewness
- J. Am. Statist. Assoc
, 1998
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Cited by 183 (11 self)
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in fat-tail Makooei breed of Iranian sheep
, 2014
"... Measurements (fat-tail dimensions ( and wool weights ..."
On Rational Bubbles and Fat Tails
- Journal of Money, Credit, and Banking
, 2002
"... Abstract: This paper addresses the statistical properties of time series driven by rational bubbles à la Blanchard and Watson (1982). Using insights on the behavior of multiplicative stochastic processes, we demonstrate that the tails of the unconditional distribution emerging from such bubble proce ..."
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processes follow power-laws (exhibit hyperbolic decline). More precisely, we find that rational bubbles predict a ‘fat ’ power tail for both the bubble component and price differences with an exponent m smaller than 1. The distribution of returns is dominated by the same power-law over an extended range
i.i.d. Random Variables with Fat Tail:
, 2011
"... estimate for distributions of the sum of i.i.d. random variables with fat tail: ..."
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estimate for distributions of the sum of i.i.d. random variables with fat tail:
Discounting with fat-tailed economic growth
- Journal of Risk and Uncertainty
, 2008
"... When the growth of aggregate consumption exhibits no serial correlation, the socially efficient discount rate is independent of the time horizon, because the wealth effect and the precautionary effect are proportional to the time horizon. In this paper, we consider alternative growth processes: an A ..."
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Cited by 26 (3 self)
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: an AR(1), a Brownian motion with unknown trend or volatility, a two-state regimeswitching model, and a model with an uncertain return of capital. All these models exhibit some persistence of shocks on the growth rate of the economy and fat tails, which implies that one should discount more distant costs
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