       Accuracy.

• To: mathgroup at smc.vnet.net
• Subject: [mg5038] Accuracy.
• From: Hyunho Shin <shinhh at plaza.snu.ac.kr>
• Date: Sat, 19 Oct 1996 16:40:38 -0400
• Organization: School of Economics, SNU.
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

In Mathematica, I run the next:

----------------------------------------------------------------------
<<Statistics`Master`

n = 500;

x2dist = NormalDistribution[1,1];
x3dist = NormalDistribution[-1,4];
udist = NormalDistribution[0,1];

x1 = Table[1, {n}];
x2 = Table[Random[x2dist], {n}];
x3 = Table[Random[x3dist], {n}];
u = Table[Random[udist], {n}];
x = Transpose[{x1, x2, x3}];
ystar = x.{1,2,3} + u;
y = Table[If[Part[ystar, i] > 0, 1, 0], {i, n}];

tol = 0.00000001;
b0 = {1,1,1};

Do[
Print[b0];
f = PDF[NormalDistribution[0,1], x.b0];
F = CDF[NormalDistribution[0,1], x.b0];
first = Inverse[Transpose[(f^2/(F(1-F)))*x].x];
second = Transpose[(f/(F(1-F)))*x].(y-F+f*x.b0);
b1 = first*second;
If[Max[Abs[b0-b1]/bo] < tol, Break[]];
b0 = b1,
{100}];

"In PROBIT Model,"
"Estimated Parameter: bprobit = " b0 ", and"

fprobit = PDF[NormalDistribution[0,1], Map[Mean, Transpose[x]].b1];

"(d F)/(d xj) = " fprobit * b0
--------------------------------------------------------------------

But I got the message:
1
Power::infy: Infinite expression -- encountered.
0.
because, in Mathematica, some elements of F are taken to 1.
But, F is a list of values of CDF of Standard Normal Distribution,
so any element of F cannot be 1.

I think Mathematica round off all elements of F,
some values, eg 0.99999999999999999999999999999999999999991, are
taken to 1's.

I want the method in which I get sufficiently accruate values,
in this context.