Poisson distribution — A detailed Guide on Poisson distribution

1. What is Poisson distribution?

The Poisson distribution is a probability distribution that simulates the possibility of seeing a certain amount of very rare events takes place over a certain amount of time or space. Its only distinguishing feature is the parameter (lambda), which denotes the average frequency of event occurrences within that interval.

The distribution offers a way to determine the probabilities of observing various numbers of events within the specified interval and is frequently used in circumstances where occurrences are independent and infrequent.

2. Why is it called Poisson distribution?

Siméon Denis Poisson, a French mathematician, is honored by having his name associated with the “Poisson distribution” word.

He developed the distribution to explain the likelihood that rare events will occur during a set period of time, making a contribution to probability theory in the 19th century. Due to his innovative work in this field, the distribution is named in his honor.

3. Why do we use Poisson distribution?

Here is a list of practical applications and reasons for using the Poisson distribution:

A. Counting Events:

The Poisson distribution is frequently used for simulating situations in which events happen at random over a certain amount of time or location.

Examples include the volume of calls a call center receives in an hour, the number of collisions that occur at a certain intersection each day, and the volume of emails that are sent each day.

B. Rare Events:

Modeling rare events that happen rarely but are still important for predicting is made possible by this technique. Equipment malfunctions, unusual diseases, or severe weather may be among those events.

C. Queuing Systems:

The Poisson distribution can be used to estimate the number of customers who will arrive within a specific time frame when evaluating queuing systems, such as the waiting areas at banks or supermarkets.

D. Epidemiology:

In epidemiology, where the number of new cases in a population can be roughly predicted by a Poisson distribution, the distribution is used to model the spread of infectious illnesses.

E. Web Traffic Analysis:

Web traffic analysis can be used to predict how many people will visit, click on, or download content from a website over a given period of time.

F. Radioactive Decay:

Nuclear physics uses the Poisson distribution to describe the quantity of radioactive particles that decay over a certain amount of time.

G. Inventory management:

The distribution helps in managing inventory levels and reorder points in cases where demand for a product is unpredictable and infrequent.

H. Quality Control:

In manufacturing, quality control can be used to examine the occurrence of defects in a production process.

I. Environmental Studies:

The number of species detected in a certain location or the frequency of events like earthquakes or meteorite impacts are both modeled using the Poisson distribution in ecology and environmental science.

J. Financial Risk Analysis:

It can be used to model unpredictable but significant events like spikes in stock prices.

K. Crime Analysis:

To determine the amount of particular crimes in particular locations, law enforcement organizations may use the Poisson distribution.

L. Sports analytics:

In sports, the distribution can be used to model how many goals, points, or scores are scored over the course of a specific amount of time.

M. Service Systems:

Businesses can use the distribution to forecast how many customer contacts or service requests will occur over a specific period of time.

N. Natural Phenomena:

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