Integration in R

[r_v.s]

I really dint know where this question should have been posted!

Is it possible to evaluate an integral in R when one of the limits is a variable?
The integration with constant limits works! If R wont do this, would you suggest a software package that would??

 

[Oxymoron]

I really dint know where this question should have been posted!

Is it possible to evaluate an integral in R when one of the limits is a variable?
The integration with constant limits works! If R wont do this, would you suggest a software package that would??

Do you mean like below? If so, MATLAB can do it.

>> syms x y
>> f = y^3 - y^2 + 1

f = y^3 - y^2 + 1

>> int(f,y,1,x)

ans = x*(x^2*(x/4 - 1/3) + 1) - 11/12

 

[r_v.s]

Yes. infact, the expression is complicated
It is a joint distribution function so, but the limits are from -infinity to x.

 

[Oxymoron]

Yes. infact, the expression is complicated
It is a joint distribution function so, but the limits are from -infinity to x.

Yup MATLAB can handle all that.

 

[Calum]

The specific code would help. I suspect it will just need a tweak to get the correct behaviour.

 

[r_v.s]

library(cubature)

k = 0.618079
rho = 0.402193
k1 = (1+s^2/4)^2.5
k2 = 4*(1-rho)^0.5

f1 = function(r,s)
{
(k*k1*(1+(r^2)/4)^2.5*(1+(s^2-2*rho*s*r+r^2)/k2)^-2.5
}
##I need to integrate the above twice from (-inf , qt(0.75,4)) wrt s and (-inf , qt(v,4)) wrt r.
Finally i require an expression in v, which i then need to integrate from (0,1).

I'd be glad of any help!

 

[Oxymoron]

library(cubature)

k = 0.618079
rho = 0.402193
k1 = (1+s^2/4)^2.5
k2 = 4*(1-rho)^0.5

f1 = function(r,s)
{
(k*k1*(1+(r^2)/4)^2.5*(1+(s^2-2*rho*s*r+r^2)/k2)^-2.5
}
##I need to integrate the above twice from (-inf , qt(0.75,4)) wrt s and (-inf , qt(v,4)) wrt r.
Finally i require an expression in v, which i then need to integrate from (0,1).

I'd be glad of any help!

What's qt(0.75,4)?

 

[Oxymoron]

If I do it from -inf to inf, MATLAB says explicit integral can't be found. Is the density correct?

 

[Calum]

k1 = (1+s^2/4)^2.5
k2 = 4*(1-rho)^0.5

These, I think, are your problem. I think you want to define k1, k2 as functions of s, as at the moment k1, k2 will just become vectors containing whatever values of s are currently in memory.

 

[r_v.s]

qt is the quantile function in r.
i just used k1 and k2 for convenience,
i've tried it with the constants plugged in, in the
equation, and was still unable to do it.

 

[r_v.s]

Is the Euler Math Toolbox a good substitute for matlab??
Any idea if it would help me??

 

[r_v.s]

Would it help to use the Ryacas package???