Poisson Distribution: Doubling Time Effects

[tutu]

Hi, in a Poisson Distribution test, what happens when the amount of time is doubled?

For example, in 1 month, lamda=np and I can calculate the probability of x events happening in that 1month.

However, if the question is changed to 6 months, what will i have to do? Thanks.

 

[mattmns]

Just multiply lambda by 6

 

[tacman]

In a Poisson Distribution, the lambda parameter represents the average number of events occurring within a given time period. So, if the amount of time is doubled, the lambda parameter will also double. This means that the average number of events occurring in the new time period will also double.

To calculate the probability of x events happening in the new time period, you will need to use the new lambda value in the Poisson formula. So, if the original lambda was np for 1 month, the new lambda for 6 months would be 2np.

In terms of doubling time, this means that the time it takes for the number of events to double will also increase. For example, if it took 1 month for 10 events to occur, it would take 6 months for 20 events to occur. This concept can be applied to any time period and lambda value.

Overall, doubling the time period in a Poisson Distribution will result in a doubling of the lambda parameter and a corresponding increase in the average number of events. It is important to adjust the lambda value accordingly in order to accurately calculate the probability of a certain number of events occurring within the new time period.