Timeline for Maximum entropy distribution with constrained quantiles
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| S Oct 30, 2022 at 12:51 | history | suggested | NunoSempere | CC BY-SA 4.0 |
Correct possible typo as indicated in the comments.
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| Oct 30, 2022 at 12:49 | review | Suggested edits | |||
| S Oct 30, 2022 at 12:51 | |||||
| Jul 8, 2021 at 7:32 | comment | added | user76284 | Did you mean to write $f(x) = \sum_i \ldots$ in your last equation? | |
| Oct 28, 2016 at 20:14 | comment | added | Nawaf Bou-Rabee | (i) Yes, that is exactly what the notation means; sorry for not defining it. (ii) The way to eliminate the $i$th Lagrange multiplier from $f(x)$ is to apply the $i$th constraint $\int_{v_{i-1}}^{v_i} f(x) dx = p_i$ which implies that $Z^{-1} \exp(\lambda_i) (v_i - v_{i-1}) = p_i$. Then use this last equation to eliminate $\exp(\lambda_i)$ from $f(x)$ to obtain the final equation given in the answer. | |
| Oct 28, 2016 at 19:43 | comment | added | mathlawguy | Thanks for the help. I'm a little confused by your answer; it is probably the result of my not being as expert in math as desirable. You appear to say at first that the maximum entropy distribution is some sort of exponential distribution in which the parameter depends on which part of the domain we are in. But then you write "Eliminating these Lagrange multipliers and writing the density in terms of the quantiles yields ... and then you have what looks to me to be a piecewise uniform distribution. How did we get from an exponential distribution to a uniform distribution? | |
| Oct 28, 2016 at 19:07 | comment | added | mathlawguy | The notation $1_[x,y]$ means a function whose value is 1 on the interval [x,y] and 0 elsewhere? | |
| Oct 28, 2016 at 18:20 | history | undeleted | Nawaf Bou-Rabee | ||
| Oct 28, 2016 at 18:20 | history | edited | Nawaf Bou-Rabee | CC BY-SA 3.0 |
added 69 characters in body
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| Oct 28, 2016 at 16:20 | history | deleted | Nawaf Bou-Rabee | via Vote | |
| Oct 28, 2016 at 16:16 | history | edited | Nawaf Bou-Rabee | CC BY-SA 3.0 |
deleted 4 characters in body
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| Oct 28, 2016 at 15:45 | history | edited | Nawaf Bou-Rabee | CC BY-SA 3.0 |
fixed a typo
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| Oct 28, 2016 at 15:28 | history | answered | Nawaf Bou-Rabee | CC BY-SA 3.0 |