How to solve a system of equations involving distribution?

 gamcdf(3.01,a,b)=0.4
 gamcdf(4.63,a,b)=0.6

how to solve for a and b?

I tried solver & evalin(symengine)

Answer 1

[Amin Zargar]

this worked:

 F = [gamcdf(6.63,x(1),x(2))-0.4;
       gamcdf(8.89,x(1),x(2))-0.6];
 x0 = [2; 0.8];            
 options=optimset('Display','iter');   
 [x,fval] = fsolve(@SPI05,x0,options)

spasiba Andrei !

[Walter Roberson]

Okay, but what do the 6.63 and 8.89 have to do with the requirements to use 3.01 and 4.63 ? And what is SPI05 ?

Also, please cross-check the solutions. When I was testing here, I found that expressing the solution in that form (as a difference), allowed an infinite number of solutions in which the gamcdf() values equations were both wrong by the same amount.

Answer 2

[Andrei Bobrov]

EDIT [20:23MSD 26.12.2011]:

fh1 = @(x)[gamcdf(3.01,x(1),x(2));gamcdf(4.63,x(1),x(2))] - [.4;.6];
out = fsolve(fh1,[1;1])

Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the default value of the function tolerance, and
the problem appears regular as measured by the gradient.

<stopping criteria details>

out =
       1.6466
       2.8322

[Amin Zargar]

Hi Andrei, I get this answer ..

Warning: Matrix is singular, close to singular or badly scaled.

Results may be inaccurate. RCOND = NaN.

> In optim\private\dogleg at 72

In optim\private\trustnleqn at 186

In fsolve at 377

No solution found.

fsolve stopped because the problem appears to be locally singular.

<stopping criteria details>

[Walter Roberson]

Amin, which MATLAB version are you using?