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Article #568

modelling distributions

#568
From: Mike Anderson
Date: Wed, 11 Nov 1992 19:47
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Suppose I have data on two variables - age and income of a person. I would like
to estimate income curves by age using spline regression, but my problem is
this: to protect the identity of the individuals, incomes were topcoded, so
that any person reporting incomes of > $100,000 gets coded at $100,000. I am
interested in getting very accurate estimates, and given the long right tail
of the income distribution, these truncated values may be throwing off my
estimates quite a bit.
	So I would like to replace the truncated values with my own "tail". My
question is, how do I go about modelling the income distribution and tacking
on my own tail? Off the top of my head, I would precede thusly: If there are
Nt truncated observations and Nu untruncated observations, N = Nt + Nu, I would
first scale the Nu incomes to mean 0, generate N obs from something like a
log-normal, lop off the top Nt quantiles, and compare the generated data to the
observed data with a Q-Q plot, choosing that level of variance in the log-normal
which gives me the straightest fit. Then I would take the Nt random values I
lopped off from the generated data and randomly assign them to the Nt truncated
values. Does this sound reasonable? I'm sure there is a better way to go about 
this, can someone tell me what it is or where to find it?
Thanks in advance, Mike Anderson
-- 
Mike Anderson    Dept. of Demography   UC Berkeley   mwande@QAL.Berkeley.EDU
"And I would say to those out around the country. 'Take a hard look now.
Don't let that rabbit be pulled out of the hat by one hand and 25 other 
rabbits dumped on you in another.'" - George Bush, 1/24/90 
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From: mwande@graunt.qal.berkeley.edu (Mike Anderson)
Newsgroups: sci.math.stat
Subject: modelling distributions
Date: 11 Nov 1992 19:47:23 GMT
Organization: University of California, Berkeley
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