Timeline for Does such probability distribution exist?
Current License: CC BY-SA 4.0
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| Jul 15, 2022 at 16:17 | comment | added | Luka74 | @Dieter Kadelka. Thank you very much for your response. Silly me. Indeed it's quite trivial. $P(X_1+X_2\leq x_0)\leq P(X_1\leq x_0)P(X_2\leq x_0)=p^2$. What I'm actually after is not necessarily $F(n,x)=F(1,X)^n$ (by $F(n,x)$ I denote the CDF of $X_1+...+X_n$), but sth that satisfies $F(n,x)=g(x)h(x)^n$ for some $g(x)$ and $h(x)$ or even more generally $F(n,x)=\sum_{i=1}^kg_i(x)h_i(x)^n$. | |
| Jul 15, 2022 at 12:47 | review | Close votes | |||
| Jul 31, 2022 at 3:03 | |||||
| Jul 15, 2022 at 12:36 | comment | added | Dieter Kadelka | There is no such distribution if $n \geq 2$. If you want to show it yourself, start with some $x_0 \in (0,\infty)$ with $0 < F(x_0) = p < 1$ and estimate $\mathbb{P}(X_1 + \ldots + X_n \leq x_0)$. | |
| Jul 15, 2022 at 12:31 | comment | added | Gerald Edgar | You are asking in the wrong forum. Nice question, anyway. | |
| S Jul 15, 2022 at 11:50 | review | First questions | |||
| Jul 15, 2022 at 12:38 | |||||
| S Jul 15, 2022 at 11:50 | history | asked | Luka74 | CC BY-SA 4.0 |