Timeline for How to calculate the sum or difference of two probability generating functions?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 21, 2023 at 13:21 | history | edited | User1865345 |
edited tags
|
|
| Apr 21, 2023 at 13:19 | comment | converted from answer | User1865345 | You can deal with a general result when you are considering convex combinations: if $\mathrm P_1, \mathrm P_2$ are probability generating functions and $\alpha\in[0, 1], $ then $\alpha\mathrm P_1 +(1-\alpha) \mathrm P_2$ is a probability generating function. It is not hard to see why: check whether the coefficients of $s^n$ in the convex combination (are non-negative, of course) sum to $1.$ Reference: Probability and Random Processes, Geoffrey Grimmett, David Stirzaker, Oxford University Press, 2020, sec. 5.1. | |
| Jun 22, 2017 at 2:38 | answer | added | Lucas Roberts | timeline score: 2 | |
| Nov 10, 2015 at 21:42 | history | edited | Glen_b | CC BY-SA 3.0 |
added 166 characters in body
|
| Nov 10, 2015 at 21:41 | comment | added | Glen_b | That independence assumption is critical; I'll edit this information into your question. | |
| Nov 10, 2015 at 17:37 | comment | added | jje | Sorry for being unclear. I was trying to ask about $G_{X+Y}$, so the PGF of the sum of $X$ and $Y$. The variables can be assumed to be independent. | |
| Nov 10, 2015 at 14:28 | comment | added | Glen_b | The sum of two functions is well defined (as is the difference); if you say "the sum of $G_X$ and $G_Y$" you're simply saying "$G_X+G_Y$" in words. What is it you actually mean to ask? Are you asking for the pgf of $X+Y$ (ie the pgf of the sum, rather than the sum of the pgfs?) | |
| Nov 10, 2015 at 9:34 | answer | added | jtobin | timeline score: 4 | |
| Nov 10, 2015 at 9:30 | answer | added | Olivier Hubert | timeline score: 1 | |
| Nov 10, 2015 at 9:08 | review | First posts | |||
| Nov 10, 2015 at 9:56 | |||||
| Nov 10, 2015 at 9:08 | history | asked | jje | CC BY-SA 3.0 |