use of dblquad with conditions over the domain of the variables.

Good afternoon,

I have the following problem,

Imagine you have 2 normal random variables, x and y, independent from each other. I want to calculate the expected value of x, given that (silly example) x*y is above 0.05.

This requires a double integral over the x and y that satisfy the condition. I tried by

Ex=dblquad(@integrand,-10,10,-10,10);

where, inside the function "integrand" I told matlab that if the condition is satisfied x*y>0.05, take the value of z=x*fx*fy, and if not z=[].

But the code does not work because dblquad does not accept empty vectors arising from "integrand".

Would you have any suggestion? A different approach?

Many thanks, Luis.

[Elif]

Hi there,

The way I see it you should explicit the constraints in the call to dblquad.

Rather than writing -10,10 call another function that captures the x and y's you want to use.

Maybe someone else can point out more about this.

Hope it helps.

[Luis]

Thanks Elif,

You mean I should do something like

dblquad(@integrand,'lowerlimitx',10,'lowerlimity',1)?

The real problem I have is a double integral where two variables are constrained i.e. x\in(4,10) and y\in(0,1). But there is another constraint because x must also be such that V(x,y)>0 as well as y itself. Does it make sense?

Answer 1

[Elif]

Ok, so clearly the outer variable depends on the inner variable and viceversa.

I think dblquad is unable in this case to obtain a solution.

You might want to consider a change of variable.