# Re: st:normal linear (mis)scaling

 From "D.Christodoulou" To statalist@hsphsun2.harvard.edu Subject Re: st:normal linear (mis)scaling Date Thu, 05 Aug 2004 14:22:33 +0100

```Nick,

- histogram normal if normal >= -0.2 | normal <=-0.8 -
to remove the exact bit that I want.

However, it is essential for this distribution to have bounds in the
interval [-1,1].
How to I restrict the random observations to be generated into this
interval.

thanks again,
Dimitris

Nick Cox wrote:
>
> I would generate lots of values from a Gaussian
> and then take a big bite out of it, with some
>
> . 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
>
> Nick
> n.j.cox@durham.ac.uk
>
> D.Christodoulou
> >
> > 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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--
---------------------------------------------
Dimitris Christodoulou
Teaching and Research Associate
School for Business and Regional Development
University of Wales, Bangor
Hen Coleg
LL57 2DG Bangor
UK
e-mail: D.Christodoulou@bangor.ac.uk
---------------------------------------------
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```