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is Poisson Distriubtion interval always time based and equal?

is Poisson Distriubtion interval always time based and equal?

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Could the interval between occurrences in the poisson distribution be anything other than time based and occur in unequal interval. if yes, are there any examples to help.
 

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365 Team
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Hey Ejike, 
Thanks for reaching out!
 
Could the interval between occurrences in the poisson distribution be anything other than time based and occur in unequal interval. if yes, are there any examples to help.
 
Shortly put – yes. We can be measuring the occurrences of something over a fixed interval of time, space of some other metric of fixed length (like a column in a dataset). 
 
For example, we can have be counting the number of cactus trees we pass by each mile, when we’re driving in Nevada. In that case the interval is distance instead of time. 
 
As for the unequal interval, it’s important to understand that lambda indicates that usual number of occurrences over a fixed interval, so if we want to examine a shorter/longer period, we need to adjust our expectation accordingly. The easiest way to do so is to change lambda proportionally to the change in the interval length and used those values for our calculations. 
 
Best, 
365 Vik

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