Is the Poisson distribution a special case of exponential distribution?

Asked Nov 15 '22 at 12:01

Active Nov 15 '22 at 13:39

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I am getting confused .How can a Poisson be a special case of exponential distribution?

edited Nov 15 '22 at 13:39

asked Nov 15 '22 at 12:01

Rohan Saha

3

It isn't. It's a member of an exponential family, which is a different thing. – Stephan Kolassa Nov 15 '22 at 12:04
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They are also connected through a Poisson process: if the gaps between events has an exponential distribution then the number of events in a time interval has a Poisson distribution. This is why the complementary CDF of an exponential distribution looks similar to the probability that a Poisson random variable is $0$. A key difference between them is that an exponential distribution is continuous while a Poisson distribution is discrete and can only take non-negative integer values. – Henry Nov 15 '22 at 12:18

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