1
$\begingroup$

My data shows the daily number of logins per person over the last three months.

I am modelling the number of events per person per day as a Poisson process. I am interested in estimating the population parameter $\lambda$ that represents the expected number of logins for any given person on any given day.

Given my data, how should I go about this? For instance, the data for the first customer (customer_id == 1) looks as follows:

customer_id date logins
1 2023-05-01 0
1 2023-05-02 2
... ... ...
1 2023-07-30 3
1 2023-07-31 1

My intuition was to simply calculate the mean of logins. However, I saw this thread and made me question if this approach is indeed the correct one.

I can see that my estimator is unbiased, but are there any downsides to simply calculating the mean? What alternatives are there?

Improve this question
$\endgroup$
2
  • 1
    $\begingroup$ Do you have a Poisson process or not? If you haven't recorded times between logons, then what about the referenced thread is applicable to your analysis? Are you perhaps intimating you would be open to estimating counts over longer periods using a Poisson assumption? $\endgroup$
    – whuber ♦
    Commented Aug 25, 2023 at 17:53
  • 1
    $\begingroup$ Agree with whuber. The Poisson process is a model for measurements/events which happen at unknown times. But you have a measurement at every day, so it seems you are in a different setting. If not, please clarify. $\endgroup$
    – picky_porpoise
    Commented Aug 27, 2023 at 9:44

1 Answer 1

Reset to default
0
$\begingroup$

In your case, if I understand you correctly, customer login (within the same day) is considered the poisson process.

Then, you might want to quickly check see if the time interval between 2 logins follows an exponential distribution. but do you have timestamp per login per customer_id?

on the other hand, if the motivation is just to get the expected number of logins for any given person on any given day. You can first take groupby average by customer_id. then check the distribution of the customer_id level lambdas. and decided whether you want further take an average to get point estimate of the lambda for the population. or give a confidence interval estimate. or even overlay other customer level data (demographics maybe) to get more insights.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.