Statistical Application in R & Python: Poisson Distribution

Continuing with the series of blogs, the first of which was Statistical Application In R & Python: Normal Probability Distribution, here we bring you a post on how you can calculate Poisson distribution effortless using R & Python. So, stay tuned!

Poisson distribution is a counting process which is a discrete probabilistic model. It has only one parameter, (lambda or “m”) which is essentially the average rate of change. Poisson distribution is used to model “number of anything”. The probability distribution function of a Poisson distribution is given by the below expression.

If m is the mean occurrence per interval, then the probability of having x occurrence with in a given interval is:

Application:

A business firm receives on an average 6.5 telephone calls per day during the time period 11:00 – 11:15 A.M., Find the probability that on a certain day, the firm receives exactly9 calls during the same period.

The random variable x is the ‘number of telephone calls received during the period 11:00 – 11:15 A.M, since x is assumed to Poisson distribution. The parameter m is equal to the mean of the distribution; i.e.  m = 6.5 and x = 9, then the equation is:

Calculate Poisson Distribution in R:

So, while calculating Poisson distribution in R, we notice that the probability of occurring exactly 9 calls instead of average 6.5 calls in a given particular time (11:00 A.M – 11:15 A.M ) = 85.81%

Calculate Poisson Distribution in Python:

So, while we calculate Poisson distribution in Python, we notice that the probability of occurring exactly 9 calls instead of average 6.5 calls in a given particular time (11:00 A.M – 11:15 A.M) = 85.81%

Conclusion:

Companies can use the Poisson distribution to contrive effective steps to improve their operational efficiency. For instance, an analysis done with the Poisson distribution might reveal how a company can arrange staffing in order to be able to handle the peak periods efficiently, when the customer service calls keep on pouring.

In this problem we see that the business firm receives on an average 6.5 telephone calls per day during the time period 11:00A.M – 11:15A.M, then the probability of the firm receives exactly 9 calls in a same is 85.81%.

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