Timeline for Iterated Kumaraswamy distributions
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 13, 2011 at 3:34 | comment | added | BSteinhurst | Only for the dependence of the stable point upon a and b, not the location of the stable point itself. I've not added an answer to this question because what I know doesn't really answer the question you asked. If you are interested in this side line feel free to contact me by e-mail though. | |
| Oct 12, 2011 at 1:47 | comment | added | OctaviaQ | @BSteinhurst: were you able to get a closed form solution? | |
| Oct 11, 2011 at 21:41 | comment | added | BSteinhurst | Ahh, I think then what I did may be tangential at best. A student and I came across not these distributions but the equations $x = 1-(1-x^{a})^{b}$ in a percolation problem. So we have some experience with the fixed points of the iteration on numbers. That all can be nicely done with a few pages of calculus. | |
| Oct 11, 2011 at 19:33 | comment | added | OctaviaQ | note: I probably shouldn't have used $a(i,a,b)$ as $a()$ is unrelated to $a$. Pretend I wrote $g(i,a,b)$ or some other unrelated letter. | |
| Oct 11, 2011 at 19:29 | comment | added | OctaviaQ | @BSteinhurst: any information at all would be great. But specifically, I am interested in calculating/comparing the mean and variance of the distributions at successive iterations. Ideally, I would love to be able to derive $a(i,a,b) = \mathbb{E}X_i$, $X_i\sim F_i$ but more realistically looking for formal proofs that the mean/variance of $F$ decreases/increases with $i$ for constraints on $a$ and $b$. | |
| Oct 11, 2011 at 18:22 | comment | added | BSteinhurst | Could you add some information about what you want specifically about the iterations? I've run into these before and could answer you better if I knew what you were looking for. | |
| Oct 11, 2011 at 2:01 | history | asked | OctaviaQ | CC BY-SA 3.0 |