Timeline for How to obtain a confidence interval for a percentile?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 27, 2022 at 2:03 | vote | accept | GeoffDS | ||
| Mar 17, 2021 at 16:00 | comment | added | whuber♦ | @Jolly You seem to be employing $u$ and $l$ asymmetrically, by subtracting $1$ in one case and not subtracting it in the other. The key, then, must lie in how you interpret my equation $(1).$ I find it's helpful to contemplate an extreme case, such as $u=n,$ and to interpret the confidence interval in that case. | |
| Mar 17, 2021 at 15:13 | comment | added | jollycat | @whuber I just read though the example in the book. You are correct with "They claim 𝑙=85 and 𝑢=97 will work." By definition, you're also right with "The expression at the left is the chance that a Binomial(𝑛,𝑞) variable has one of the values {𝑙,𝑙+1,…,𝑢−1}". Yet, I don't understand why the book uses a CI of [x_l, x_u] but computes the confidence level with B(u - 1, 100, 0.9) - B(l - 1, 100, 0.9). With a CI of [x_l, x_u] , I was expecting B(u, 100, 0.9) - B(l - 1, 100, 0.9). (Or a CI of [x_l, x_{u-1}] would work with B(u - 1, 100, 0.9) - B(l - 1, 100, 0.9) ). | |
| Mar 17, 2021 at 13:21 | comment | added | whuber♦ | @jollycat It's easy to make one-off mistakes like that, but I recall being careful not to and careful with the example and the software to match the book. I cannot find the explanation to which you refer. A close look at the plot shows it colors the cases 85 through 96, inclusive, in cyan; and my explanation explicitly characterizes the upper tail as "97 or more." This doesn't appear to match what you or retodomax seem to be saying. | |
| Mar 17, 2021 at 12:46 | comment | added | jollycat | @whuber, I second the point by retodomax: You're contradicting yourself in the explanation and the example. Explanation: "The expression at the left is the chance that a Binomial(𝑛,𝑞) variable has one of the values {𝑙,𝑙+1,…,𝑢−1}". Example: you're given 𝑙=85 and 𝑢=97. But then the values included in your interval are {𝑙,𝑙+1,…,𝑢} instead of {𝑙,𝑙+1,…,𝑢−1}. | |
| Mar 8, 2021 at 16:12 | comment | added | retodomax | As I understand, ${l, l+1, \dots, u-1}$ are all "plausible values" for a random variable following a Binomial(n,q) distribution. $u$ is not included and therefore, it is unlikely to observe $u$ observations which are less than or equal to the quantile. Still, we use $X_{u}$ as our upper bound and not $X_{u-1}$? | |
| Mar 8, 2021 at 14:35 | comment | added | whuber♦ | @retodomax I'm afraid I don't understand your argument, perhaps because what you mean by "plausible values" is unclear. | |
| Mar 8, 2021 at 8:10 | comment | added | retodomax | $u-1$ would be in the range of plausible values for number of $X_i$ less than or equal to $F^{-1}(q)$, whereas $u$ is not. Why do we take $X_{(u)}$ as the upper limit and not $X_{(u-1)}$. Would the CI not be conservative otherwise? | |
| Jun 12, 2017 at 16:41 | history | answered | whuber♦ | CC BY-SA 3.0 |