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This may be a silly question, but if we look at Poisson distribution at $k = \mu$ and $k = \mu-1$, for integer $ \mu $ the values are nearly identical.

from scipy.stats import poisson

poisson.pmf(k=5, mu=5)
Out[39]: 0.17546736976785068

poisson.pmf(k=4, mu=5)
Out[40]: 0.17546736976785063

Should this be interpreted as arrival of 4 events has similar probability as arrival of 5 events given a common rate of 5 events per period or population? This breaks my intuition, why so?

Evgeny
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    When λ is a positive integer, the modes are λ and λ − 1. – user2974951 Jan 13 '21 at 11:56
  • I think the answer to my question is here, using the modes terminology: https://stats.stackexchange.com/questions/210475/why-two-modes-for-a-poisson-distribution-with-lambda-an-integer – Evgeny Jan 13 '21 at 14:20

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