Recent content by Hejdun

Yes, it is this that I was looking for, which I believe does not exist for the integral that started this thread. Thanks for your replies.

Not exactly the same but an expression somewhat similar. Does your solution work? This is when substituing exp(x)/(1+exp(x))^2 with normal pdf?

It is a component in the covariance matrix of a logistic regression following a specific data generating process. Anyway, I solved the problem somehow by approximating exp(x)/(1+exp(x))^2 with a mixed normal distribution. This works terrific actually! The "only" issue now is how to select the...

It seems that there is no analyc answer to this integral since integration will result in an error function. But thanks anyway!

Mathematica reports: NMinimize::nnum: The function value Uz is not a number at {v,vz1,vz2} = {0.652468,1.26614,1.36563} but I don't see the error. The restrictions are necessary, but I will try you suggestion!Edit: Now I tried the following code below and although I got several error messages...

Consider the functions g(x)=e^x/(1+e^x)^2 and f(x) = vf_1(x) + (1-v)f_2(x) . where f_1(x)=\dfrac{1}{\sqrt{2\pi\sigma^2_1}}e^{-\dfrac{x^2}{2\sigma^2_1}},\,\,\, f_2(x)=\dfrac{1}{\sqrt{2\pi\sigma^2_2}}e^{-\dfrac{x^2}{2\sigma^2_2}} and -\infty < x < \infty, \,\,\, 0 < v < 1, \,\,\...

I will try integration by parts, but I am not sure if that would solve it. No, unfortunately it is from 0 to ∞. Otherwise it would have been a standard result.

This is (perhaps) a tricky question regarding the moment of normal distribution. Let f(x) be the pdf of normal distribution with mean (-σ^2/b) and variance σ^2, where b is just a constant. The goal is to solve the integral ∫ x^3 f(x) dx integrating from 0 to ∞. I am stuck. Any...

I tried the pdf of a normal distribution instead of exp(X)/(1+exp(X))^2 and it seems to work quite well.

Alright, I was wrong regarding the expectation not being finite. Still, I have tried various things but are not able to solve it. Not even with the hints above, trying to do integration by parts. Due to the function being even, I used focused on the positive part of the domain and instead of...

Thanks for the replies! I am still working on this integral, but it seems that the expectation is infinite. I will be back giving a more thorough explanation.

Hi everyone, I have been struggling with an expectation for a while. It is seems very difficult (if not impossible) to find an analytical expression, but all hints and suggestions would be most appreciated. Here goes. I want to find an analytical expression (i.e. solve the integral) for the...

Because this expectation is a part of a larger derivation of a proof and needs to be more general. But thanks for you comment.

Thanks for your answer. That is true. I think the assumption Y(Z)=Y(-Z) could be wrong however (even though they are very similar), since when I run simulations to check E(Y) then E(Y) ≠ 0.

Thanks again for you interest in my problem and your suggestions. However, I am not sure how your suggestion in this case would help. What chi-square distribution and how many degrees of freedom? BTW, I tried doing a Padé Approximation instead of Taylor expansion, but that didn't help...