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st: normal linear (mis)scaling

From   "D.Christodoulou" <>
Subject   st: normal linear (mis)scaling
Date   Thu, 05 Aug 2004 13:47:18 +0100

Dear Statalisters,

I need to illustrate the failure of the normal distribution, in terms of
linear scaling, to describe a distribution with fairly distinguished

To go tto he extreme and make this more obvious, I consider the following
Let assume a sample of 1000 observations which are distributed in a [-1, 1]
interval. Suppose that there is a large but smoothly distributed cluster of
900 observations that take values in the [-0.2, 1] interval, and the rest
of the 100 observations lie in the [-1, -0.8] interval. Thirty percent of
the linear scaling will be used for non-existent values. The normal
distribution will fit a large volume of variation in that gap.
(The example is merely to make clear the possibility of mis-scaling and how
it works, I'm not bothered with the obvious mixture of distributions)

I need to generate the appropriate data and do this on a graph, e.g. a
histogram with a superimposed normal density (the graph is not a problem).
I have been playing around with the -invnorm(uniform())- function to
generate the data but I didnt even get near to what I want to do. Any
suggestions are gratefully appreciated!

many thanks in advance,

Dimitris Christodoulou
Teaching and Research Associate
School for Business and Regional Development
University of Wales, Bangor
Hen Coleg
LL57 2DG Bangor
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