How do I model a Paretian Distribution in Excel?

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Guest

Stock returns more closely resemble a Paretian Distribution (fat tails) than
a normal or lognormal distribution. Is there anyway to model this
distribution in Excel?
 
Thanks, but I'm not sure this is what I'm after. While I think the name may
refer to Pareto, I've always seen it referenced as a Paretian distribution
rather than a Pareto distribution and the shape of the Pareto distribution is
not what I expected. I think these are two different distributions, even if
both eminate from Pareto. I do know that a Paretian distribution has no
standard deviation for example, and it should have negative values on the
left.
 
I had never heard of a "Paretian distribution", but a Google search found
some relevant hits.

According to
http://www.riskglossary.com/articles/cauchy_distribution.htm
Student's t distribution with 1 degree of freedom (also known as the Cauchy
distribution) is an example of a stable Paretian distribution.

According to
http://www.riskglossary.com/articles/stable_paretian_distributions.htm
Mandelbrot coined the term Paretian for leptokurtic (fat tailed)
distributions. Why he muddied the waters by creating a new synonym for an
existing term is unclear. It also notes that a stable distribution is one
with the property that sums of iid random variables can be linearly scaled to
reproduce the original distribution. Only three closed forms for stable
distributions are known:
- Normal (not leptokurtic)
- Cauchy (Student's t with 1 df)
- Levy (only positive x)
You can easily work with the Cauchy distribution in Excel. Otherwise you
will need to learn a good bit of math, begining with the theory of
characteristic functions of a distribution.

Jerry
 
Jerry W. Lewis said:
According to
http://www.riskglossary.com/articles/stable_paretian_distributions.htm
Mandelbrot coined the term Paretian for leptokurtic (fat tailed)
distributions. Why he muddied the waters by creating a new synonym for an
existing term is unclear.
Click to expand...

On further reflection, the reason he coined a new term is that leptokuric
implies the existence of the first four moments, whereas the Cauchy
distribution is so fat tailed that not even the first moment exists.

Jerry
 
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