How to code integral of product of lognormal variables?

1 次查看（过去 30 天）

VS 2022-11-16

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1852423-how-to-code-integral-of-product-of-lognormal-variables

编辑： Torsten 2022-11-16

I am trying to code integral of a product of variables which follow different distributions. Here's a simple example:

where b is a scalar (let's say 0.65), ϵ and z are lognormal variables, and σ is a variable that follows Uniform distribution. Here,

is a particular value that σ takes which comes from solving another equation not shown here. How can I code this expression? How can I handle a variable integral limit in such cases (

in this example)?

回答（1 个）

Askic V 2022-11-16

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1852423-how-to-code-integral-of-product-of-lognormal-variables#answer_1101348

在 MATLAB Online 中打开

Please have a look at how this example would be solved in Matlab:

syms x y z;
f = @(x,y,z) 2*x.*exp(y).*sin(z); % define the input function
Q = integral3(f,1,2,0,1,0,pi)
Q = 10.3097

Thanks @Torsten. Is there a way to handle variable integral limit in multiple integration? I have multiple integrals whose lower or upper limit is a variable that I obtain by solving another equation.

Torsten 2022-11-16

编辑：Torsten 2022-11-16

在 MATLAB Online 中打开

Yes, define the integral as a function of the limit and evaluate the integral when the limit becomes known as a numerical value.

Or use symbolic computations with the limit as a symbolic variable. If you are lucky, the symbolic toolbox will be able to compute the integral involving the symbolic limit variable.

syms a b c x lb ub

f = a*x^2+b*x+c;

F = int(f,x,lb,ub)

F =