Poisson Distribution Calculator

How does this Poisson distribution calculator work?

The Poisson distribution refers to a discrete probability distribution that expresses the probability of a specific number of events to take place in a fixed interval of time and/or space assuming that these events take place with a given average rate and independently of the time since the occurrence of the last event.

This Poisson distribution calculator uses the formula explained below to estimate the individual probability:

P(x; μ) = (e^-μ) (μ^x) / x!

Where:

x = Poisson random variable.

μ = Average rate of success.

e = e constant equal to 2.71828...

P = Poisson probability.

Based on this equation the following cumulative probabilities are calculated:

1) CP for P(x < x given) is the sum of probabilities obtained for all cases from x= 0 to x given - 1.

2) CP for P(x ≤ x given) represents the sum of probabilities for all cases from x = 0 to x given.

3) CP for P(x > x given) is equal to 1 - P(x ≤ x given).

4) CP for P(x ≥ x given) is P(x = x given) + P(x > x given).

Where:

CP = Cumulative Probability

Example of a calculation

Let’s consider that in average within a year there are 10 days with extreme weather problems in United States. So what is the probability that United States will face such events for 15 days in the next year?

In this case:

Random variable [x] = 15

Average rate of success [μ] = 10

Finally we obtain:

■ Poisson Probability - P(x = 15) is 0.034718 (3.47%)

■ CP - P(x < 15) is 0.916542 (91.65%)

■ CP - P(x ≤ 15) is 0.951260 (95.13%)

■ CP - P(x > 15) is 0.048740 (4.87%)

■ CP - P(x ≥ 15) is 0.083458 (8.35%)