Timeline for Probability that a sum is less that a given value [closed]
Current License: CC BY-SA 3.0
13 events
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| Aug 13, 2016 at 21:41 | comment | added | RaduB | I searched on Google and I found something like my question in physics.harvard.edu/uploads/files/undergrad/probweek/sol38.pdf and in mathworld.wolfram.com/UniformSumDistribution.html, but I don't have enough knowledges to adapt them. And, regarding your last question, I am sure that I'm not interrested to aproximate it when m is close to 0. Thank you again! | |
| Aug 13, 2016 at 21:37 | comment | added | RaduB | Thank you very much Douglas for your interrest! You're right about my method of generation: I take all the numbers from 1 to n and I put each in one of k bins. The $n_1,...,n_k$ are the count of values placed in each bin. It's a part of a graph algorithm. | |
| Aug 13, 2016 at 18:11 | comment | added | Douglas Zare | The next question would be, "Where do you want to approximate it?" and then perhaps, "How well would you like to approximate it?" If you say, "Everywhere! Perfectly!" then you shouldn't expect to get an answer. When you have a complicated function, it is often difficult to approximate it everywhere, but much easier to pick a place and approximate it there. Are you interested in the case that $m$ is close to $0$? That $m$ is close to the average value (whatever that is)? That $m$ is close to $n \choose 2$? It might be that very different techniques would be applied in different locations. | |
| Aug 13, 2016 at 18:09 | comment | added | Douglas Zare | Further, you say "calculate" which suggests that you need an exact answer, probably in closed form. However, I wouldn't expect any natural, nontrivial distribution to have such a closed form expression for the probability that $\sum {n_i \choose 2} \ge m$. I suspect an approximation would be fine. Maybe say what you need this for? | |
| Aug 13, 2016 at 17:59 | comment | added | Douglas Zare | If you generate each $n_i$ uniformly, they probably won't add up to $n$. Let me mention a completely different and very natural way to get a multiset of $k$ numbers adding up to $n$: Generate a random function from $\{1,2,...,n\}$ to $\{1,2,...,k\}$. Let $n_i$ be the count of the elements sent to $i$. The uniform distribution and this distribution will have quite different probabilities. | |
| Aug 13, 2016 at 15:05 | comment | added | RaduB | Sorry for my mistake. I am programmer and I have only few knowledges about probabilities. I think that the distribution of ${n_1,...,n_k}$ is an uniform one as I generate them using a good PRNG, isn't? | |
| Aug 13, 2016 at 10:53 | history | closed |
Douglas Zare Wolfgang Franz Lemmermeyer Stefan Kohl♦ Myshkin |
Needs details or clarity | |
| Aug 13, 2016 at 8:35 | review | Close votes | |||
| Aug 13, 2016 at 10:53 | |||||
| Aug 13, 2016 at 7:51 | comment | added | Douglas Zare | Of course the distribution is necessary to calculate or estimate the probability. If you don't have a distribution in mind, then you don't have a question. | |
| Aug 13, 2016 at 6:20 | comment | added | RaduB | I have no specific distribution on the multiset ${n_1,...,n_k}$, but, if is mandatory in order to calculate the probability, you can assume one. Thank you! | |
| Aug 12, 2016 at 21:05 | review | First posts | |||
| Aug 12, 2016 at 21:12 | |||||
| Aug 12, 2016 at 21:00 | comment | added | Douglas Zare | What distribution do you have on the set/multiset $\{n_1,...,n_k\}$? | |
| Aug 12, 2016 at 20:58 | history | asked | RaduB | CC BY-SA 3.0 |