This book has been written for numerate non-specialists and serves three purposes. Firstly, it gathers together mathematical material from diverse but related fields of order statistics, records, extreme value theory, majorization, regular variation and subexponentiality. Secondly, it presents a new measure of obesity. Thirdly, and most importantly, the authors hope to convince readers that fat-tail […]
This book has been written for numerate non-specialists and serves three purposes.
Firstly, it gathers together mathematical material from diverse but related fields of order statistics, records, extreme value theory, majorization, regular variation and subexponentiality. Secondly, it presents a new measure of obesity. Thirdly, and most importantly, the authors hope to convince readers that fat-tail phenomena pose real problems; they are really out there and they seriously challenge our usual ways of thinking about historical averages, outliers, trends, regression coefficients and confidence bounds among many other things. Data on flood insurance claims, crop loss claims, hospital discharge bills, precipitation, and damages and fatalities from natural catastrophes drive this point home.
While most fat-tailed distributions are “bad”, research into fat tails is one distribution whose tail will hopefully get fatter.