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                                       Details van artikel 13 van 21 gevonden artikelen
 
 
  Optimizing Linear Functions of Random Variables having a Joint Multinomial or Multivariate Normal Distribution
 
 
Titel: Optimizing Linear Functions of Random Variables having a Joint Multinomial or Multivariate Normal Distribution
Auteur: Reyes, J. P. De Los
Verschenen in: Communications in statistics
Paginering: Jaargang 18 (1989) nr. 3 pagina's 835-856
Jaar: 1989
Inhoud: A computer method to find vectors s that minimize [image omitted]   (ci>0 constants) subject to a probability constraint P{μi≤si, i=1,…,r}≥1-α (≤α≤1) where v,…,vr have a joint multinomial distribution, is obtained by solving the corresponding optimization problem through the usual normal approximation. Thus vectors [image omitted]   are sought that minimize [image omitted]   (bi>0 constants) subject to a multivariate normal probability constraint [image omitted]   where v1,…,vr have a joint singular multivariate normal distribution. The singular normal probability integral [image omitted]  is expressed in various computer-ready formulas as: (a) one integral over a simplex, (b) a sum of integral over multidimensional rectangular regions, and (c) a sum of integrals over multidimensional right triangles or plane orthoschemes. The optimization of F, and thereby of G, is accomplished using a known nonlinear program in conjunction with also known numerical multivariate normal distribution computer codes which work well for r=3. Binomial tables and a bisection method may be used for r=2. However for r≥4, the optimization routine requires many function evaluations of[image omitted]  , making the solution somewhat difficult and expensive while theoretically simple and feasible. In this regard an approximation with Bonferroni bounds to evaluate [image omitted]   is derived and is shown to be accurate to within ±.005 for values of xi such that [image omitted]   , in the equicorrelated-equicoordinate case, namely, xi=x and [image omitted]   , i=1,…,r.
Uitgever: Taylor & Francis
Bronbestand: Elektronische Wetenschappelijke Tijdschriften
 
 

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