The Poisson distribution represents the probability distribution of a certain number of events occurring in a fixed time interval. The events tend to have a constant mean rate. Poisson distribution is further used to determine how many times an event is likely to occur within a given time period. The range of Poisson distribution starts at zero, and it goes until infinity. In Poisson distribution, the rate at which the events occur must be constant, and the occurrence of one event must not affect the occurrence of any other event, i.e., the events should occur independently.
Examples of Poisson Distribution
1. Number of Network Failures per Week
Poisson distribution is used by cell phone companies and wireless service providers to improve their efficiency and customer satisfaction ratio. Provided that the history of the number of network failures occurring in the locality in a particular time duration is well known, the probability of a certain number of network failures occurring in future can be determined easily with the help of Poisson distribution. This helps the broadcasting organisations be prepared for the problems that might occur and draft the solution in advance, so that the customers accessing their services don’t have to suffer the inconvenience.
2. Number of Bankruptcies Filed per Month
Poisson distribution finds its prime application in the banking sector. It is usually used to determine the probability of customer bankruptcies that may occur in a given time. For instance, if the bank records show that each month in a particular locality on average four bankruptcies are being filed, then this information can be used to estimate the probability of zero, one, two, or three bankruptcies may be filed in the following month. This helps the bank managers estimate the amount of reserve cash that is required to be handy in case a certain number of bankruptcies occur.
3. Number of Website Visitors per Hour
The number of visitors visiting a website per hour can range from zero to infinity. Since the event can occur within a range that extends until infinity, the Poisson probability distribution is most suited to calculate the probability of occurrence of certain events. For instance, if the number of people visiting a particular website is 50 per hour, then the probability that more or less than 50 people would visit the same website in the next hour can be calculated in advance with the help of Poisson distribution. Once the probability of visitors about to visit a particular website is known, the chances of website crash can be calculated. The site engineer, therefore, tends to maintain the data uploading and downloading speed at an adequate level, assigns an appropriate bandwidth that ensures handling of a proper number of visitors, and varies website parameters such as processing capacity accordingly so that website crashes can be avoided.
4. Number of Arrivals at a Restaurant
Restaurants employ Poisson distribution to roughly estimate the number of customers that are expected to visit the restaurant on a particular day. Let us say that every day 100 people visit a particular restaurant, then the Poisson distribution can be used to estimate that the next day, there are chances of more or less than 100 people visiting that particular restaurant. This helps the owner get an idea of the number of people visiting his/her restaurant, and what amount of raw material would be required for their service.
5. Number of Calls per Hour at a Call Center
The concept of Poisson’s distribution is highly used by the call centres to compute the number of employees required to be hired for a particular job. For instance, if the number of calls attended per hour at a call centre is known to be 10, then the Poisson formula can be used to calculate the probability of the organisation receiving zero calls, one call, two calls, three calls, and any other integer number of calls per hour, thereby allowing the managers to have a clear idea of the number of calls required to be catered at different hours of the day and helps to form a proper schedule to be followed by the employees accordingly.
6. Number of Books Sold per Week
If the number of books sold by a bookseller in a week is already known, then one can easily predict the number of books that he might be able to sell next week. For this purpose, the person tends to access the already known data or the information regarding sales of the bookstore and calculates the probability of selling a certain number of books in a definite or fixed duration of time with the help of Poisson distribution.
7. Average Number of Storms in a City
Poisson distribution finds its prime application in predicting natural calamities in advance. The risk estimation helps the environmental engineers and scientists take suitable measures to prevent loss of lives and minimize property destruction to a significant extent. For this purpose, the average number of storms or other disasters occurring in a locality in a given amount of time is recorded. The recorded data acts as the information, which is fed to the Poisson distribution calculator. The calculations give the probability of a certain number of calamities that may occur in the same locality in near future.
8. Number of Emergency Calls Received by a Hospital Every Minute
If we know the average number of emergency calls received by a hospital every minute, then Poisson distribution can be used to find out the number of emergency calls that the hospital might receive in the next hour. This helps the staff be ready for every possible emergency.