Timeline for Does anyone recognize the following theorem on probability distributions?
Current License: CC BY-SA 4.0
6 events
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Jun 6, 2023 at 23:29 | comment | added | Iosif Pinelis | In fact, if $X$ has the chi-squared distribution, then this distribution (or any distribution, which is a measure) cannot be the number $f_n(x)$ or even a function $f_n$. Also, then $(n/2)1/2(X−1)$ cannot have a normal distribution, whatever $n$ is doing. This is not just a question of having clear definitions. Without clear definitions, no proofs are possible. Accordingly, the claims you make in your post can be true only under certain conditions, not stated by you at all (if they can ever be true). | |
Jun 6, 2023 at 21:04 | comment | added | Iosif Pinelis | Then, what does "$(n/2)1/2(X−1)$ has a normal distribution when $n\to\infty$" mean? | |
Jun 6, 2023 at 19:50 | comment | added | Carlo Beenakker | if $X$ has the chi-squared distribution $f_n(x)$, then $(n/2)^{1/2}(X-1)$ has a normal distribution when $n\rightarrow\infty$ | |
Jun 6, 2023 at 18:47 | comment | added | Iosif Pinelis | What does "$f_{n}(x)\mapsto \sqrt{\frac{n}{4\pi}}e^{-(n/4)(x-1)^2}$" mean (mathematically)? | |
Jun 5, 2023 at 11:26 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
added 16 characters in body
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Jun 5, 2023 at 11:17 | history | answered | Carlo Beenakker | CC BY-SA 4.0 |