Introduction to Poisson Distribution
In statistics, a Poisson distribution shows how many times an event is expected to occur within a particularised period. In other terms, it is a count distribution. These help with understanding independent events at a constant rate within a provided interval of time. It was named after the French mathematician Siméon Denis Poisson.
Understanding Poisson Distributions
Poisson distribution can estimate how likely it is that an event will happen "X" number of times. For example, suppose the average number of people who rent movies on a Friday night at a single video store location is 400. In that case, a Poisson distribution can answer questions like, "What is the probability that more than 500 people will rent movies?" Therefore, the application of the Poisson distribution allows managers to introduce optimal scheduling systems that would not work with, say, a normal distribution.
One of the most famous historical, practical uses of the Poisson distribution was determining the annual number of Prussian cavalry soldiers killed by horse-kicks. Other modern examples involve assessing the number of car crashes in a city of a given size.
Business Uses Of The Poisson Distribution
Here are some ways that a company might use analysis with the Poisson Distribution.
Monitor for adequate customer service staffing- Calculate the average number of customer service calls each hour that need more than 10 minutes to handle. Then, calculate the Poisson Distribution to obtain the probable maximum number of calls each hour that might come in expecting more than ten minutes to run.
Using the Poisson formula to assess whether it is financially viable to keep a store open 24 hours a day- Calculate the average number of sales executed by the store during the overnight shift – the period from midnight till 8 A.M. Using the distribution formula, calculate the probable least number of sales that might be made during the overnight shift. Finally, determine whether that lowest probable sales figure depicts sufficient revenue to cover all the costs of keeping the store open through that period while also providing a reasonable profit.
Evaluate business insurance coverage - Determine the average number of losses or claims that occur every year and covered by the company's business insurance. Do a Poisson probability calculation to evaluate the maximum and minimum numbers of claims that might fairly be filed during any one year.
