🚀 go-pugleaf

conoverj@vaxb.acs.unt.edu writes:


>I am looking for algorithms to find the maximum or
>minimum of n randomly distributed normals.  Does
>anyone know of a site for source code for this problem? 

I assume that you mean that you are looking for approximations to the
distribution of the maximum.  Simulation of the maximum of n randomly
distributed normals is straightforward.  Look in any book on random
number generation for methods to simulate independent normals.

>Is the method 
>used by Clark (1961) used by anyone?  The citation that
>I have is Operations Research, March-April 1961, Charles
>E. Clark, "The Greatest of a Finite Set of Random Variables."

The Clark method has been used occasionally by econometricians for
approximating choice probabilities in the multinomial probit model.
The current fashion is to approximate these probabilities using Monte
Carlo integration methods.  There is a paper by Lerman and Manski
(reference follows) that reports on some numerical experiments testing
the quality of Clark's approximation and comparing it to simulation
approximations.  They also provide a brief, informal explanation of
the Clark approximation.

The reference is:

"On the Use of Simulated Frequencies to Approximate Choice
Probabilities," by Steven R. Lerman and Charles F. Manski, chapter 7
in _Structural_Analysis_of_Discrete_Data_with_Econometric_
_Applications_, Charles F. Manski and Daniel McFadden (eds.), M.I.T.
Press, 1981.

T. Scott Thompson
University of Minnesota
thompson@atlas.socsci.umn.edu