Timeline for Sample standard deviation is a biased estimator: Details in calculating the bias of $s$
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Nov 3, 2020 at 7:41 | comment | added | Darya | @angryavian I am bit unclear on this, but will follow-up with a new post. Thanks very much | |
| Nov 3, 2020 at 6:35 | comment | added | angryavian | @Darya In that context, the square root in $\sqrt{S^2}$ is defined to be the positive square root. | |
| Nov 3, 2020 at 5:53 | comment | added | Darya | @angryavian thanks, it's all much clearer now. Just another question not directly related to this (but related to the original post), in the derivation of this expression, why was it assumed that E(S) is positive. (the sqrt of the variance can give both positive and negative values)? | |
| Nov 2, 2020 at 2:36 | vote | accept | Darya | ||
| Nov 1, 2020 at 19:39 | comment | added | angryavian | @Darya Updated my answer to address your first question. For your second question, I made an error and have corrected it. | |
| Nov 1, 2020 at 19:38 | history | edited | angryavian | CC BY-SA 4.0 |
added 270 characters in body
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| Nov 1, 2020 at 7:02 | comment | added | Darya | @angryavian (i) when I substitute n=2x-1 into sqrt(2/(n-1), I get sqrt(1/x). (ii) could you also please show how we get 1/4n from the last line? When I plug in x=(n/2)-1 into the extreme lower right term i.e. 1/(2x+1), I get n + (1/2). (My maths level is not advanced so apologies if this may be a bit basic) | |
| Oct 31, 2020 at 17:44 | comment | added | angryavian | @Darya It comes from the $\sqrt{\frac{2}{n-1}}$ term in your original expression. | |
| Oct 31, 2020 at 16:38 | comment | added | BruceET | Elegant, Nice (+1) | |
| Oct 31, 2020 at 8:08 | comment | added | Darya | In the 1st line, how do we get the additional sqrt(x+1/2) in the denominator? I just get Gamma(x+1)/Gamma(x+(1/2)) when I substitute x=(n/2) -1 | |
| Oct 31, 2020 at 6:21 | history | answered | angryavian | CC BY-SA 4.0 |