{"id":110719,"date":"2025-08-04T15:39:41","date_gmt":"2025-08-04T10:09:41","guid":{"rendered":"https:\/\/www.mygreatlearning.com\/blog\/poisson-distribution\/"},"modified":"2025-08-04T14:44:04","modified_gmt":"2025-08-04T09:14:04","slug":"poisson-distribution","status":"publish","type":"post","link":"https:\/\/www.mygreatlearning.com\/blog\/poisson-distribution\/","title":{"rendered":"When and How to Use Poisson Distribution in Data Analysis"},"content":{"rendered":"\n

By: Prof. Mukesh Rao<\/a> (Senior Faculty, Academics, Great Learning)<\/strong><\/p>\n\n\n\n

The Poisson distribution is a discrete probability distribution model that helps quantify events that occur over a specific interval of time, space, or volume. It is particularly useful when analyzing counts, such as defects, website visits, or customer arrivals.<\/p>\n\n\n\n

This model represents processes that generate information in the form of counts, i.e., integer values. For example, the number of defects per unit output. The occurrence of a defective piece is an event of interest. The Poisson distribution can be studied on the time axis, in space, or even in volume.<\/p>\n\n\n\n

Let\u2019s dive into understanding why the Poisson distribution is used in data analysis.<\/p>\n\n\n\n

What is the Poisson Distribution?<\/h2>\n\n\n\n

Poisson Distribution is a discrete probability distribution. This model represents processes that generate information in counts, i.e., integer values. For example, the number of defects per unit output.<\/p>\n\n\n\n

Imagine a chip manufacturing unit. We wish to establish the capability of the process. For this, we gather information from the production line. We collected fifty samples. Those which were defective have a red dot and other not. The occurrence of a defective piece is an event of interest. From now onwards, we will refer to events.<\/p>\n\n\n\n

Suppose we observed 25 defective units out of the 50 inspected. Is there a pattern hidden in this data? Or are these defective pieces randomly scattered? If there is a pattern, we can model it and, as discussed earlier, use the model to assess the capability of the process quantitatively. To explore any possible pattern, we analyse the data at a block level instead of individual pieces.<\/p>\n\n\n\n

Suppose we pack six output units into one block as shown below. Assuming each output is generated at fixed time interval, each block is six time units long (period).<\/p>\n\n\n\n

Poisson distribution can be studied on time axis, space or even volume. In this example, we are analysing it on time axis.<\/p>\n\n\n

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The first observation we can make is, the average number of defectives per time interval (of six units), represented by \u028e is 3. Note: average per time interval is 3 does not mean every time interval will have exactly 3 events.<\/p>\n\n\n\n

Variance across time intervals is also 3 (how?). We know \u028e = 3, use the formula for variance, and check out (remember, variance is an average metric, i.e., on average, how much a data point varies from the central value (\u028e) that represents the entire data distribution.<\/p>\n\n\n\n

Given the information on the average and variance, we can find the probability of K events per interval using the formula \u2013<\/p>\n\n\n

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