Timeline for Sample Size for Exponential Distribution
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 31, 2020 at 16:51 | vote | accept | anon | ||
| Mar 31, 2020 at 14:20 | comment | added | Stephan Kolassa | Thanks. I consolidated my comments into an answer so we can take this off the "unanswered questions" list. | |
| Mar 31, 2020 at 14:19 | answer | added | Stephan Kolassa | timeline score: 0 | |
| Mar 31, 2020 at 11:14 | comment | added | anon | Ok, perfect. Now that you mention it, not sure why I didn't think of multiplying the expectation by k. I will check out your other suggestions. Thanks for the help! | |
| Mar 30, 2020 at 14:43 | comment | added | Stephan Kolassa | Finally, I do a lot of demand forecasting. My first reaction was, to be honest, that assessing CIs for an iid assumption is not what you should be doing. In sales, you typically have strongly nonstationary series, which include all kinds of multiple-seasonalities, price/promotion as a driver etc. Are you sure you are complexifying your approach in the right direction? | |
| Mar 30, 2020 at 14:41 | comment | added | Stephan Kolassa | It may also be helpful to note that the sum of $k$ iid exponentials with mean $\lambda$ is Erlang distributed with parameters $k$ and $\lambda$. The quantiles from the Erlang may be what you are looking for. | |
| Mar 30, 2020 at 14:40 | comment | added | Stephan Kolassa | If you are interested in confidence intervals for this mean, the uncertainty comes exclusively from the uncertainty in your estimates for the exponential. I don't think there is a closed formula for how this carries through, and in any case, if I understand you correctly, you are treating your fitted exponential as fixed, so under this assumption, there is no relevant CI any more. If you want to relax that assumption (and you probably should), then I would bootstrap the entire estimation procedure before taking means. | |
| Mar 30, 2020 at 14:37 | comment | added | Stephan Kolassa | OK, thanks. In that case, the mean of the sum of $k$ iid variables is just $k$ times the mean of each variable, so you can simply take the expectation of your fitted exponential distribution and multiply by $k$. Any particular reason why you are not doing this? | |
| Mar 30, 2020 at 13:32 | comment | added | anon | @StephanKolassa Yes, exactly. | |
| Mar 30, 2020 at 12:51 | comment | added | Stephan Kolassa | My understanding: you have historical observations that you assume are iid from an exponential distribution. Correct? You wish to have an estimate for the sum of $k$ samples from this distribution, if possible with a confidence interval. Also correct? | |
| Mar 30, 2020 at 12:35 | review | First posts | |||
| Mar 30, 2020 at 20:30 | |||||
| Mar 30, 2020 at 12:31 | history | asked | anon | CC BY-SA 4.0 |