How can I generate events using the Poisson distribution in R?

Question

How can I generate events using the Poisson distribution in R? The events could be the occurrence of floods in the next 1000 years at a given rate of occurrence per year.

I will be very impressed the first time a thousand-year flood is attributed to somebody's R code. Then we will really know we're in the Matrix. :-) — whuber, May 23 '13 at 13:16
Do you want to generate the times of the individual events, or the total number of events in 1000 years, or some other quantity? — Glen_b, May 24 '13 at 07:44
@ Glen_b I would want to generate the times of individual events — Bhekimpilo Ndlovu, May 27 '13 at 12:41

score 3 · Answer 1 · answered Dec 11 '15 at 13:33

3

The following gives you one inter-event time

 - log(runif(1)) / lambda

where lambda is the intensity of your Poisson process so the time-series of times of n events is obtained as:

cumsum(-log(runif(n))/lambda)

answered Dec 11 '15 at 13:33

mts

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or use the built-in cumsum(rexp(n,lambda)) – Ben Bolker Dec 11 '15 at 14:43
@BenBolker Wouldn't that be simply a uniform distribution? – Liran Funaro Jan 06 '19 at 16:18
I'm not sure why you think so. rexp(n,lambda) generates n random exponential deviates with rate parameter lambda, the same as -log(runif(n))/lambda – Ben Bolker Jan 06 '19 at 16:30

score 2 · Answer 2 · answered Jun 22 '13 at 18:52

2

How about

rate   <- 0.123456
period <- 1000
start  <- 2013.5
floods <- runif(rpois(1,period*rate), min=start, max=start+period)

since the dates are uniformly distributed within the time interval

answered Jun 22 '13 at 18:52

Henry

39,459

score 0 · Answer 3 · edited Jun 22 '13 at 19:14

0

You should use the command rpois(n, 1000*lambda), where lambda is the average number of occurrences per year (and hence the occurrence in 1000 years should be 1000 times more), and n is the number of random values to return.

edited Jun 22 '13 at 19:14

Nick Cox

56,404
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answered May 23 '13 at 14:17

Linda H

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Wouldn't these be counts of floods during 1000 years, and not the events (or at least their times) themselves? What you need to make progress with this question is the relationship between the Poisson distribution for counts and the Exponential waiting time between them. – whuber May 23 '13 at 15:08
1

Thank you for the response Linda H,@ whuber I think its the count of events, I would need to have the times the events would occur instead.Thank you for the insights – Bhekimpilo Ndlovu May 27 '13 at 12:40

How can I generate events using the Poisson distribution in R?

3 Answers3