# Create Poisson distribution

I would like to make a phone call at the average arrival rate of λ = 300 [call / minute] per minute in the Poisson distribution of the telephone exchange and save it on the list.

I don't know even if I look at the site. Give me advice. Thank you.

As simple calculation, you can do something like this to simulate a sequence of calls. The list returned gives the times of calls.

SeedRandom[1];
With[{callRate = 300, nCalls = 10},
Accumulate @ RandomVariate[PoissonDistribution[callRate], nCalls]]


{318, 634, 920, 1222, 1517, 1801, 2097, 2428, 2717, 3021}

Note: I only use SeedRandom[1] to get reproducible results, so that others can check my work.

However, you are likely to want to make many such lists, so I recommend converting the calculation to a function. Like so:

calls[
callRate_?NumberQ /; callRate > 0/callRate,
nCalls_Integer /; nCalls > 0] :=
Accumulate @ RandomVariate[PoissonDistribution[callRate], nCalls]


Then

eedRandom[1]; calls[300, 10]


gives

{318, 634, 920, 1222, 1517, 1801, 2097, 2428, 2717, 3021}

• thank you very much for advice! – Kenta Kawai Feb 14 '19 at 7:41