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st: RE: normal linear (mis)scaling

From   "Nick Cox" <[email protected]>
To   <[email protected]>
Subject   st: RE: normal linear (mis)scaling
Date   Thu, 5 Aug 2004 13:55:50 +0100

I would generate lots of values from a Gaussian 
and then take a big bite out of it, with some 
randomness about the biting. 

. set obs 1000 
. gen normal = invnorm(uniform()) 
. qnorm normal
. histogram normal if (abs(normal) * uniform()) > 0.5 
. histogram normal if (abs(normal) * uniform()) > 0.6

[email protected] 

> I need to illustrate the failure of the normal distribution, 
> in terms of
> linear scaling, to describe a distribution with fairly distinguished
> clusters.
> To go tto he extreme and make this more obvious, I consider 
> the following
> illustration:
> 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!

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