A continuous variable with a long tail distribution
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See also: Splicing
Distributions window
What do we mean by a long-tailed
distribution? One distribution is said to have a longer tail than another
if its probability density (or mass) function is (asymptotically) larger
than the other distribution's for very large values of the variable, i.e.
for two distributions A and B:
Many socioeconomic and other natural random
variables take long-tailed distributions. Examples are city population
sizes, occurrences of natural resources (e.g. size of reserves in a certain
geological region), stock price fluctuations, size of companies, income.
The most commonly fitted
distribution to the extreme of such data has been the Pareto.
There is no decent theory to explain why the Pareto distribution tends
to fit the tails of long-tailed variables, but most people accept that
it works and use it anyway.
The Pareto is usually a poor fit for the main
body of the variable, though. Thus, when modelling long-tailed distributions
one usually does so using a splice of one distribution (like the Lognormal,
or Gamma,
for example), with a Pareto distribution to model the tail.
In ModelRisk you can use the Splicing
Distributions window to splice two distributions together.
