I'm working on a scenario where I have to generate some numbers at a rate of 10, use cumsum to sequence them, and then remove anything with a value over 12 (this represents the timings of visitors to a website):
Visits = rexp(4000, rate = 10)
Sequenced = cumsum(Visits)
Sequenced <- Sequenced[Sequenced <= 12]
From here I need to verify that the generated "visits" follows a Poisson process with a rate of 10, but I'm not sure I'm doing this right.
TheMean = mean(Sequenced)
HourlyRate1 = TheMean/12 # divided by 12 as data contains up to 12 hours
This does not generate an answer of (or near) 10 (I thought it would based on the rate parameter of the rexp function).
I am new to this, so I believe I have misunderstood something along the way, but I'm not sure what. Can somebody please point me in the right direction, where using the data generated in the first code segment above, I need to "verify the visits follow a Poisson Process with rate λ equals 10".
You are measuring the wrong thing.
Since Sequenced (the times of visits) cannot exceed 12, its mean is likely to be about 6 and, if that is the case, it simply confirms that you applied that limit of 12
What does have a Poisson distribution is the number of terms in Sequenced: this is expected to be 12×10=120 though with a variance of 120 and so a standard deviation of 10.95. You could look at that, or divide that by 12 (in which case the expected value is 10 and standard deviation about 0.9, but that is not Poisson distributed and has the possibility of non-integer values), with the R code
NumberOfVisits <- length(Sequenced)
VisitsPerUnitTime <- NumberOfVisits / 12