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RE: st: from normal to bimodal distribution


From   Linn Renée Naper <linn.naper@ecgroup.no>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: from normal to bimodal distribution
Date   Mon, 17 Nov 2008 16:17:59 +0100

Hi

The command from you Maarten works well with regard to generating a new variable with a 
bimodal distribution. 

I have generated a bimodal variable, one for each observation, 
and then added it to the original price. 

But, I am still not sure how adding this kind of variable to the original prices will help me 
to change the distribution in the way I want to. 
At least I haven't yet figured out exactly how this may be done.

I want to "force" the old prices into having a "new distributional shape" with two peaks, 
but I do not necessarily want to change the global mean very much. My prices have the 
following distribution (in case it may be useful to know in order to comment on this):


  variable |      mean       min       max        sd  variance       p25       p50       p75
-------------+--------------------------------------------------------------------------------
       mip |  60.28128  8.918235  776.2332  39.47987   1558.66  36.53056  48.77862  69.81553
----------------------------------------------------------------------------------------------

I realize that the distribution of the "new prices" 
will vary with how I define means and sd of the bimodal variable. 

Moreover, the prices will be changed randomly even though the changes are 
drawn from a bimodal distribution, so what I might need is some weighting of the observations
in order to get the "shape" that I want.

Alternatively, is there a way to for example redefine the percentiles in an 
already existing distribution perhaps? Or in some other way imposing the distributional change 
directly to the original data (the original price)?


Thanks


-----Opprinnelig melding-----
Fra: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] På vegne av Maarten buis
Sendt: 17. november 2008 11:45
Til: statalist@hsphsun2.harvard.edu
Emne: Re: st: from normal to bimodal distribution

--- Linn Renée Naper <linn.naper@ecgroup.no> wrote:
> How do I tell Stata to draw random variables or generate a stochastic
> variable with a bimodal distribution? Can the rnd-command by Hilde be
> used?

You can create a mixture of Gaussian (normal) distributions, like in
the example below: the local p represents the probability of belonging
to group 1, the locals mu1 and mu2 represents the means of group 1 and
2 respectively, and the locals sd1 and sd2 the standard deviations in
group 1 and group 2. 

*--------------- begin example -----------------
drop _all
set obs 10000

local p = .5

local sd1 = .75
local sd2 = 1.5

local mu1 = -2
local mu2 = 2

gen u = uniform()
gen e = invnorm(uniform()) * ///
        cond(u < `p', `sd1', `sd2') + ///
        cond(u < `p', `mu1', `mu2')

hist e
*---------------- end example ---------------------
(For more on how to use examples I sent to the Statalist, see
http://home.fsw.vu.nl/m.buis/stata/exampleFAQ.html )

Hope this helps,
Maarten


-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

visiting address:
Buitenveldertselaan 3 (Metropolitan), room N515

+31 20 5986715

http://home.fsw.vu.nl/m.buis/
-----------------------------------------


      
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