From: John Conover <john@email.johncon.com>

Subject: Re: lognormal distribution and brownian motion

Date: 3 Dec 2001 09:24:50 -0000

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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