I want to estimate a simple variable: "**how many times my website is visited in 2015?".

Suppose that I cannot count all visits to my website (it is expensive!), but I can count the connections on smaller periods: i.e. in s% of times, I resume the counter and record the number of visits.

For example, I record the number of visits to my website every hour, but only from x:00 to x:06 which means a $s=10\%$ sample. Then I can multiply my counts to $1/s$ in order to get the estimate of the total visits.

The questions is: Assume that the number of visit is $N$, then what is the minimum sampling rate (or sample size) (with 95% confidence interval) so that the error is less than $\epsilon=1\%$?

P.S. Assume that the recording times are random (e.g. in every minute, we turn on the counter with $s\%$ probability..

  • $\begingroup$ I don't understand how it could cost you money to count visitors to your website. Don't you already your web server's logs from every visit in 2015? There's no sense in estimating something statistically when you can easily measure it directly. $\endgroup$ Jun 27, 2016 at 22:19
  • $\begingroup$ @Kodiologist it is obviousely a toy example, the main problem is somthing llike, say, counting the traffic of each website in and ISP's router, where I can analyze only a few packets. I want to know how can I estimate the count of a measure with confidence when the recordings are occasionally. $\endgroup$
    – Ali
    Jun 27, 2016 at 23:01


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