Timeline for The Number of Exponential Summands in a Fixed Interval is Poisson
Current License: CC BY-SA 3.0
8 events
when toggle format | what | by | license | comment | |
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May 31, 2016 at 14:32 | comment | added | whuber♦ | I don't know, because I invented it to answer this question. A little research suggests it is closely associated with the differential-difference equations derived for birth-death processes (but IMHO leads to a simpler analysis and an easier solution). It is also an example of a continuous-time Markov process. That should give you a set of effective search terms. | |
May 31, 2016 at 14:22 | comment | added | Taylor | Where can I learn more about this sliding window approach to examining stochastic processes? | |
May 30, 2016 at 17:48 | comment | added | whuber♦ | It is true that the numbers of points in two overlapping intervals will not be independent. However, this lack of independence does not affect any analysis based on expectations. | |
May 30, 2016 at 17:46 | comment | added | Taylor | There's one parenthetical comment early on in the Poisson process section that says something like "independent of" which threw me off | |
May 30, 2016 at 17:41 | comment | added | whuber♦ |
You could do either, but I'm actually "sliding" it in the sense of letting it have any real value of $1$ or greater. This appears in the theoretical treatment (I integrate over $t$, rather than sum over it) and in the code (ecdf , the empirical cumulative distribution function, considers all real values of its arguments, not just integral values).
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May 30, 2016 at 16:46 | vote | accept | Taylor | ||
May 30, 2016 at 16:46 | comment | added | Taylor | So you're not sliding $t$, you're incrementing it by $1$ every time, right? I'm going to accept the answer, but I might have some questions later on. | |
May 29, 2016 at 16:30 | history | answered | whuber♦ | CC BY-SA 3.0 |