solving an equation involving an integral

[Philippe Rous]

Hi everybody !

(X, Y) are jointly distributed as Normal(mux, muy, Omega). mux, muy and omega are known.

Let pdf(x,y) the normal bivariate probability distribution function of (X,Y)

I have to solve for the unknown parameter "a" in the attached equation where all is known but "a"

Is there anyway to get the value of "a" ?

Thanks a lot !

Phil

[trubador]

That would require a specialized math software. If you have "biprobit" user object installed in EViews, then you can do the following approximation:

Code: Select all

mode quiet scalar a call find(a,1.957,0.958,0.7,-3,1e-06,1e-05) subroutine local find(scalar !a, scalar !b,scalar !q, scalar !rho, scalar !lbound, scalar !tol, scalar !step) while @abs(@cbvnorm(!lbound,!b,!rho)-!q)>!tol !lbound=!lbound+!step wend !a = !lbound endsub

Inputs are in terms of standardized variables, and !rho is the correlation. !q is the resulting probability, !b is the upper limit of second variable and !lbound is the lower bound for first variable that the search will begin. You can decide the level of precision by changing the tolerance (!tol) as well as the step size (!step).