🚀 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

thompson@atlas.socsci.umn.edu (T. Scott Thompson) writes:

>conoverj@vaxb.acs.unt.edu writes:
 This is me on a different account!

>>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
 Yes, this is what I was after.

>>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.
  Thanks for this reference, it is checked out of our library
  at the moment (I checked before I posted, but I did not know its
  importance since I could not read it).  Does anyone know of source
  code on this problem?  

  I am trying to replicate the work in Boyle and Tse, Journal of
  Financial and Quantitative Analysis, Vol. 25, No. 2. June 1990,
  " An Algorithm for Computing Values of Options on the Maximum
    or Minimum of Several Assets".  This work can be used for
  valuing real options such as multiple use machine tools.  The
  full problem that I am trying to tackle is:  How much should
  flexible manufacturing tools sell for?  Suppose that the machine
  can turn out any of N outputs from a set of M inputs.  Most of the
  work to date states that you cannot pay too much for such a machine.
  In fact, negative net present value projects become "with much 
   hand-waving" positive NPV projects (if measured correctly!).
   I am trying to remove the hand-waving from the process since
   it is difficult to judge how hard and how long the hands 
   should flap.

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

James A. Conover
University of North Texas
fg33@sol.acs.unt.edu