Poisson Calculator

Using the Poisson Distribution Calculator

This guide will walk you through the steps to effectively use the Poisson Distribution Calculator to determine the probability of a number of events occurring within a fixed interval of time or space.

Step 1: Understand the Inputs

The calculator requires three primary inputs:

• Average Rate (λ): Enter the expected number of occurrences within the given interval. This input is required, and the value should be a non-negative number. You can enter values up to two decimal places for precision.
• Number of Events (k): Specify the exact number of occurrences you are interested in. This input is also required and must be a non-negative integer.
• Calculation Type: Choose whether you want to calculate the exact probability of exactly k events occurring (Exact Probability P(X = k)) or the cumulative probability of up to and including k events (Cumulative Probability P(X ≤ k)).

Step 2: Enter Your Data

Fill in the input fields:

1. Lambda: Input the average rate of events (λ) in the designated field. Ensure that the number is realistic for the context you are considering.
2. Number of Events: In the k field, type the number of times the event is observed or expected.
3. Calculation Type: Select either ‘Exact’ or ‘Cumulative’ from the options provided, based on your requirement.

Step 3: Interpret the Results

Upon entering the required data, the calculator will compute several values related to the Poisson distribution:

• Probability: This is the probability of k events occurring, formatted as a decimal with six decimal places. For an ‘Exact’ calculation, it is the probability of exactly k events. For a ‘Cumulative’ calculation, it is the probability of up to and including k events.
• Probability Percentage: Displayed as a percentage, this converts the probability into a more interpretable format, with four decimal places for accuracy.
• Mean (λ): This is the average rate of events, represented again to confirm input and calculated to two decimal places.
• Variance: In a Poisson distribution, the variance is equal to the mean, and is shown with two decimal points precision.
• Standard Deviation: It equals the square root of the mean, giving you a measure of the spread of the distribution, calculated to three decimal places.

Step 4: Analyzing the Output

Use the results to understand the likelihood of the number of events or make decisions based on the cumulative probabilities. These insights can guide actions or predict future occurrences in scenarios where such probabilistic assessments are vital.

The Poisson Distribution Calculator is a powerful tool for statistical analysis, providing both clarity and detail to effectively interpret Poisson-distributed events.