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[Fwd: mills]


-- 
Gerard Jungman <jungman@lanl.gov>
Los Alamos National Laboratory
--- Begin Message --- Dear Mr. Yonta and Mr. Jungman,
I found your messages on Internet:
In the modelling one economic situation I came to the following problem:
I am interested in equation:
(a-x)F(x)=f(x),
where f(x) pdf for normal standard distribution. F(x) - cdf.
a is a positive constant:
So I have something like Mills ratio. (a-x)=f/F:
I am interested in this equation - positive and negative solutions.
Does it have a unique solution? Perhaps it depends on a:
This solution is bigger or less than the mean (0)? Again it may depends on magnitude of a.


How to compare (a-x)F(x) with f(x) when x is negative?
Obviously LHS has one maximum: and when a is bigger than 2 only one positive solution. But I am not sure about negative solutions.


If a is less than 2 perhaps we again should distiguish between two cases a is bigger or less than 1/2:

I will be very appreciate your help,
Best regards,
Aggey Semenov, University Toulouse 1, Economic department:


--- End Message ---

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