From: John Conover <john@email.johncon.com>
Subject: Re: Plain English Pareto 80/20 explanation ?
Date: 20 Oct 1999 04:55:42 -0000
Robert Vienneau writes:
> In article <7uf9et$838$1@minus.oleane.net>, "Yann" <ygourven@webcom.com> wrote:
>
> > Could anyone explain to me why the 80/20 rule always apply. In plain English
> > if possible.
>
> I don't have an English language explanation.
>
> However, are you aware that there's a generalization in the form of
> a complete probability distribution, the Pareto distribution? The
> Pareto distribution is commonly used in, for example, reliability
> engineering.
>
In a Brownian motion fractal model of things like industrial markets,
wealth, stock prices, economics systems, (and, as R. Vienneau
mentions, mechanical, structural, and, electrical failures,) etc., the
magnitude of something happening is inversely proportional to the
number of times that the something happened, ie., a frequency
distribution of 1 / f^2 for Brownian models, although most things
economic have exponents slightly greater than 2, (ie., fractional
Brownian motion.)
The distribution of wealth in the US, from the 1997 US Budget at
http://cher.eda.doc.gov/BudgetFY97/index.htm, shows about an 80/20
rule, and about a 1 / f^2, frequency distribution of wealth, (ie., how
many folks have that much much wealth.)
Struggling through the integration from +infinity to zero, gives about
an 80/20 rule, (actually, 84/16.)
The 1 / f^2 frequency distribution is related to the zero crossing,
and run lengths, of things like recessions and depressions, stock
prices, etc., ie., the chances of a run length continuing will be
proportional to the reciprocal of sqrt (t), the chances of a zero
crossing goes up with the sqrt (t), and the deviation from "average"
proportional to sqrt (t), (for t >> 1.) At least as a first order
model of a lot of economic things, the sqrt and 1 / f stuff are neatly
tied up together by the fractal sciences. A better approximation is,
as mentioned, the Pareto distribution which has 1 / f^n, with n
usually greater than 2 for economic things.
For particulars, Manfred Schroeder, "Fractals, Chaos, Power Laws",
W. H. Freeman and Company, New York, New York, 1991, ISBN
0-7167-2136-8, pp. 126-130, might be of some help, and gives an
intuitive presentation.
John
--
John Conover, john@email.johncon.com, http://www.johncon.com/