Timeline for Approximation to ratio distribution
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
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| May 19, 2023 at 22:11 | vote | accept | Hazards | ||
| May 19, 2023 at 1:45 | comment | added | Iosif Pinelis | @Hazards : The concern about statistics has been fully addressed at the end of the answer. Can we now wrap up this matter? | |
| May 17, 2023 at 1:19 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| May 16, 2023 at 21:51 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| May 16, 2023 at 21:50 | comment | added | Iosif Pinelis | @JamesMartin : I think your concern about statistics has now been fully addressed at the end of the answer. Are you now quite satisfied with the answer? | |
| May 16, 2023 at 21:45 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| May 16, 2023 at 8:32 | comment | added | James Martin | I agree the OP did not specify what is meant by "obtain". The question was how to "obtain" the distribution of $Y$ from samples of $X$ and $Z$. From independent finite samples from $X$ and $Z$ of any size, there is no way to get an exact sample from $Y$ -- for example you can't distinguish with certainty between a distribution putting all its mass on the point $1$ and one putting all its mass on $2$. So then, in what sense might one "obtain" $\mathcal{Y}$ from such a sample? The interpretation about estimates which get more reliable as the samples get bigger was my attempt at that. | |
| May 16, 2023 at 8:26 | comment | added | James Martin | I don't think the "statistics" part that you added is right. The property that $XY\sim \mathcal{Z}$ for independent $X\sim \mathcal{X}$ and $Y\sim\mathcal{Y}$, does not imply that $Z/X\sim\mathcal{Y}$ for independent $X\sim\mathcal{X}$ and $Z\sim\mathcal{Z}$. | |
| May 15, 2023 at 22:55 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| May 15, 2023 at 22:51 | comment | added | Iosif Pinelis | I have now added something on the "positive" side of the matter, and also on statistics. | |
| May 15, 2023 at 22:49 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| May 15, 2023 at 22:33 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| May 15, 2023 at 22:30 | comment | added | Iosif Pinelis | @JamesMartin : Where in the OP do you see "how do we go about getting estimates on the distribution of $Y$ which get more reliable as our samples get bigger?"? The questions that I can see in the OP were "can I obtain $\mathcal{Y}$? Are there any results/papers on this?", and these questions have been answered. | |
| May 15, 2023 at 20:41 | comment | added | Hazards | @JamesMartin +1 Indeed, although not clear from my side, the question is coming from a statistics/sampling point of view | |
| May 15, 2023 at 20:25 | comment | added | James Martin | Nice example! - but also was that really the whole question? The question seemed to me to have a more statistical flavour - supposing we have access not to complete information about the distributions of $X$ and $Z$, but to samples, how do we go about getting estimates on the distribution of $Y$ which get more reliable as our samples get bigger? Of course, in a case like the one you mention where the distribution of $Y$ is not uniquely determined, it's problematic.... but what about in a "nice case"? | |
| May 15, 2023 at 20:05 | comment | added | Hazards | Thanks a lot for taking the time to answer my question! Do you think we could impose some special restrictions on the formulation of the distributions of $Z$ and $X$ such that we can uniquely determine $Y$? I.e. does there exists a class of distributions for which we could determine this? | |
| May 15, 2023 at 19:24 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |