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- From: Agguei Semenov <agguei dot semenov at univ-tlse1 dot fr>
- To: yonta at yorku dot ca
- Cc: jungman at lanl dot gov
- Date: Fri, 03 Oct 2003 15:35:51 +0200
- Subject: mills
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:
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