[Scilab-users] n dimensional normal distribution

[Samuel Gougeon]

Hello Masahiro,

Le 18/03/2018 à 17:31, fujimoto2005 a écrit :
> Let x1, x2, .., xn be an random variable of n dimensional normal
> distribution. Is there any function that gives the probability of {x1> =
> k1}&{x2> = k2}&...&{xn> = kn}?

I thougth at the first sight that it would be possible to get this 
probability with some lexicographic sorting, but it's not the case. I 
don't thing that we can avoid an explicit loop. Here is a possible 
direct calculation, from a list of actual samples :

ns  =  20;     // number of samples
nd  =  3;      // number of dimensions
k  =  [5  3  7];
m  =  grand(ns,nd,"nor",8,3)
for  i  =  1:nd
     [?,r]  =  gsort(m(:,i));
     m  =  m(r,:);
     m  =  m(find(m(:,i)>=k(i)),:)
end
p  =  size(m,1)/ns   // requested probability

Example of run :
  m  =
    12.750144   7.1200267   5.900484
    12.575508   5.410083    10.976422
    12.399993   3.7475677   10.092495
    12.220889   5.4940195   6.1479044
    12.158487   5.2062957   11.651957
    11.611694   6.6661928   5.9750098
    10.718146   2.2454739   11.737011
    10.343892   4.2714818   4.7199587
    9.9907016   7.7903253   5.9802778
    8.3135823   4.8094984   7.1769228
    8.0939865   9.2484944   13.215993
    8.0098652   3.0198012   7.5767533
    7.5354006   10.715856   8.985266
    7.4971339   17.821625   5.5456382
    6.6502306   8.7791304   8.812858
    6.5728805   12.299302   7.9823783
    6.2940806   10.376389   7.8221558
    5.2862072   6.0566186   11.102784

  m  =
    7.4971339   17.821625   5.5456382
    6.5728805   12.299302   7.9823783
    7.5354006   10.715856   8.985266
    6.2940806   10.376389   7.8221558
    8.0939865   9.2484944   13.215993
    6.6502306   8.7791304   8.812858
    9.9907016   7.7903253   5.9802778
    12.750144   7.1200267   5.900484
    11.611694   6.6661928   5.9750098
    5.2862072   6.0566186   11.102784
    12.220889   5.4940195   6.1479044
    12.575508   5.410083    10.976422
    12.158487   5.2062957   11.651957
    8.3135823   4.8094984   7.1769228
    10.343892   4.2714818   4.7199587

  m  =
    8.0939865   9.2484944   13.215993
    12.158487   5.2062957   11.651957
    5.2862072   6.0566186   11.102784
    12.575508   5.410083    10.976422
    7.5354006   10.715856   8.985266
    6.6502306   8.7791304   8.812858


--> p = size(m,1)/ns  // requested probability
  p  =
    0.3

Samuel

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