# Re: lognormal distribution and brownian motion

From: John Conover <john@email.johncon.com>
Subject: Re: lognormal distribution and brownian motion
Date: 3 Dec 2001 09:24:50 -0000

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The discreet time function:

v    = v  (1 + R )
t+1    t       t

where R  is a function of a random variable with a Gaussian/Normal
t
distribution, (with a standard deviation of about 0.02, and a mean of
about 0.0004 for things economic on daily scales,) models many
things-like personal wealth over a lifetime, stock values, etc.

If many such functions make up an aggregate, the frequency
distribution of the aggregate is a lognomal distribution, like the
distribution of wealth in a society, or the distribution of stock
values in an exchange.

If such a frequency distribution of the aggregate is plotted against
the log of the abscissa, it is a Gaussian/Normal distribution.

The distribution of the sum of all agents in the aggregate, like the
index of a stock exchange or GDP will be leptokurtotic, i.e.,
non-Gaussian/Normal with fat tails.

John

BTW, there are C sources to programs that will provide some intuition
at:

http://www.johncon.com/ntropix/utilities.html

Robert Vienneau writes:
> In article <9suaeo\$e27\$02\$1@news.t-online.com>, "Marco Gerlach"
> <marcogerlach@web.de> wrote:
>
> > Another question by the way: Can somehome tell me, where i can find an
> > interesting and elementary treatment of the properties of the lognormal
> > distribution?
> > Thank you!
>
> The lognormal distribution is used in reliability and maintainability
> engineering. Thus, any intro text in R&M from a statistics perspective
> should treat the lognormal distribution. A some old example is
> Mann, Schafer, and Singpurwalla.
>
--

John Conover, john@email.johncon.com, http://www.johncon.com/

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