Question

Present three different expressions for the Poisson distribution, based on different contexts (comm systems, epidemiology, traffic flow, failure rate,etc.) Explain the differences in parameter definition.

Answer 1

Example 1 - Average number of flights taking off an airport per hour.

Let's say that about 6 flights take off on an average every hour from New Delhi international airport. So, the average number of flights taking off any hour can be modelled as a poisson distribution with parameter = 6 given as -

-----------------------------------------------------------

Example 2 - Average number of calls arriving every 5 min at a call center.

Let's say that about 8 calls arrive every 5 mins at a call center service. As each call arrives independently, so the distribution of number of calls arriving every 5 mins can be modelled as a poisson distribution with parameter = 8 given as -

--------------------------------------------------------------

Example 3 - Average number of earthquakes occuring in Japan everyday.

Japan has a surprisingly high rate of approximately 4 earthquakes occuring every day. So, average number of earthquakes on any day in Japan can be modelled using poisson distribution with paramter = 4 given as -

_____________________________

_________________________________________________

In first example, the parameter can be defined as "Average number of flights taking off from New Delhi International Airport" every hour.

In second example, the parameter can be defined as "Average number of calls that arrive at a given call center every 5 mins".

And in third example, it can be defined as "Average number of earthquakes occuring in Japan on any given day".

There is a a basic difference in the way these parameters are defined. Note that all of them have different time frame. The first one averaged for an hour, second one for every 5 mins and the last one for every day. So, the parameter of poisson distribution varies with time frame we are interested in and depending on situation the time frame can be adjusted to meet our requirement.