Maximum Likelihood Estimation

    {  like.mpl  }

    {  GAMS Model Library, http://www.gams.com/modlib/libhtml/like.htm  }

    {  Maximum Likelihood Estimation,  NLP,  Size: 3x9  }




TITLE
    Like;

OPTIONS
    ModelType=Nonlinear
    ParserType=Extended

INDEX
    i := 1..31;
    g := 1..3;

DATA
    Y[i]  := ( 95,105,110,115,120,125,130,135,140,145,
              150,155,160,165,170,175,180,185,190,195,
              200,205,210,215,220,225,230,235,240,245,260);
    W[i]  := ( 1, 1, 4, 4,15,15,15,13,21,12,17, 4,20, 8,17,
               8, 6, 6, 7, 4, 3, 3, 8, 1, 6, 0, 5, 1, 7, 1, 2);
    C     := 1/((2*3.14159)^0.5);
    E     := 2.718282;
    OrdG[g] := ord(g);
    MlwBd[g] := FORMULA(100+30*OrdG);

VARIABLES
    P[g] INITIAL 0.3333;
    M[g] INITIAL MlwBd;
    S[g] INITIAL 15;

MODEL

    MAX Mlf = SUM(i: W * log(C * SUM(g: P/S * E^(-0.5*((Y-M)/S)^2))));


SUBJECT TO

     PDef:   SUM(g: P) = 1;

     Rank[g>1]: M >= M[g-1];

BOUNDS
     0.1 <= P <= 10000;
     0 <= M <= 10000;
     0 <= S <= 10000;
END