How to prove arrival rate follows Exponential Distributions?

I'm studying Anylogic. I'm curious about something. Some people explain that arrival rate follows Exponential Distribution. I wanna know 'How can prove that?'

Any kind guidance from you would be very helpful and much appreciated. Thank you so much.

Solution

The arrival rate doesn't follow an exponential distribution, it follows a poisson distribution, so there's nothing to prove on that regard.

What follows an exponential distribution is the inter-arrival time between agents.

To prove that this thing actually follows a particular distribution, you can use one of the many distribution fitting techniques out there, my favorite and the one is the Cullen and Frey Graph. You can see an answer about it here:

https://stats.stackexchange.com/questions/333495/fitting-a-probability-distribution-and-understanding-the-cullen-and-frey-graph

You can also check the wikipedia page on distribution fitting: https://en.wikipedia.org/wiki/Probability_distribution_fitting

Have in mind that distribution fitting is kinda an art, and no technique gives you the correct distribution, but maybe a good enough approximation of a distribution. But in this case it should be quite easy.

You can't really prove that a distribution fits the data though, you can just have maybe an error estimation when you compare the distribution function with the actual data, and you can have a confidence interval for that... I'm not sure if that's what you want.