# Cumulative Poisson Distribution Calculator

Analyze data using the cumulative Poisson distribution with our calculator.

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Use this Cumulative Poisson Distribution Calculator to determine the cumulative probability of a Poisson-distributed random variable falling below a certain value. The Poisson distribution is commonly used to model the number of events that occur within a fixed interval of time or space, given a known average rate of occurrence.

## Calculating Cumulative Poisson Distribution

To calculate the cumulative Poisson distribution, you’ll need two key inputs:

**Rate (λ):**The average rate of occurrence of events in the given time or space interval.**Number of Events (k):**The maximum number of events below which you want to calculate the cumulative probability.

The formula for calculating the cumulative Poisson distribution is as follows:

**Cumulative Probability (P(X ≤ k)) = ∑ [e^(-λ) * (λ^x) / x!], where x ranges from 0 to k**

## Using the Calculator

Simply enter the rate (λ) and the desired number of events (k) into the calculator, and it will provide you with the cumulative probability that X is less than or equal to k.

Understanding the cumulative Poisson distribution can be invaluable in various fields, such as finance, science, and quality control, for predicting rare events and making informed decisions.