Timeline for Deconvolution of gamma distributions
Current License: CC BY-SA 2.5
11 events
| when toggle format | what | by | license | comment | |
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| Nov 19, 2009 at 21:03 | history | edited | George Lowther | CC BY-SA 2.5 |
added to Edit 2
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| Nov 18, 2009 at 12:53 | comment | added | Trevor Stewart | Thanks, George. I'll work through this. Looks like an ingenious solution. | |
| Nov 18, 2009 at 2:08 | comment | added | George Lowther | Further to my comment above, the more general example in my second edit can also be understood in terms of local times of Brownian motion. X_A is the local time at 0 of a Brownian motion B while its maximum process B*(t)=max_{s<=t}B(s) is in A. | |
| Nov 18, 2009 at 1:56 | history | edited | George Lowther | CC BY-SA 2.5 |
added more general example; added 9 characters in body
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| Nov 17, 2009 at 23:18 | history | edited | George Lowther | CC BY-SA 2.5 |
added edit in response to Michael Lugo; added 4 characters in body; added 1 characters in body
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| Nov 17, 2009 at 23:05 | comment | added | George Lowther | Thanks, Michael, I fixed my post. I suppose you could further decompose X in a similar way to get a sum of as many independent rvs as you like, and them rearrange them into two terms neither of which are gamma distributed. | |
| Nov 17, 2009 at 23:03 | history | edited | George Lowther | CC BY-SA 2.5 |
fixed mistake
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| Nov 17, 2009 at 23:01 | comment | added | Michael Lugo | Actually, A is gamma-distributed here, with k = 1. But B isn't, so this is still a counterexample. | |
| Nov 17, 2009 at 22:59 | comment | added | George Lowther | Some background on where my example came from: I know that the local time at 0 of a Brownian motion B at the first time it hits 1 has the exponential distribution. If you understand these concepts, then it is easy to see that it is the sum of the local time at 0 at which B first hits 1/2 plus the local time at 0 of the BM started at 1/2 when it first hits 1. These are independent, and the second has a prob of 1/2 of being 0, so can't be gamma distributed. I just converted this example into a simple argument using moment generating functions. | |
| Nov 17, 2009 at 22:44 | history | edited | George Lowther | CC BY-SA 2.5 |
characteristic function -> moment generating function
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| Nov 17, 2009 at 22:39 | history | answered | George Lowther | CC BY-SA 2.5 |