Skip to content

Home / Statistical Tools / Distribution Fit/Calc / Distribution Calculator / Poisson Distribution

Poisson Distribution

Probability Calculator

From Excel click...

QXL Stat Tools Tab > Distribution Fit/Calc > Distribution Calculator > Poisson

The Poisson distribution is a discrete probability distribution. The Poisson distribution is used to calculate the probability of a number of events occurring based upon the probability of a single event. The Poisson distribution has two parameters. Lambda is the mean rate of occurrence of an event. The Poisson distribution assumes that the rate of occurrence is independent and constant. The second parameter is gamma (threshold or offset), which is sometimes used in Monte Carlo simulation studies to shift the distribution right or left.

PoissonDist

Using the Calculator

Step 1

Enter the mean (lambda), the rate of occurrence. Optionally, enter the offset (threshold).

Step 2

Quantum XL will plot the probability X starting at 1.

If X was supplied:

  • The bar corresponding to X will be red.

  • At the bottom of the report, Quantum XL will provide the numeric results for X being less than, less than or equal to, greater than, greater than or equal to, and equal to.

Understanding the Results

In 2004, Central Florida was blasted by Hurricanes Charley, Frances, Ivan, and finally Jeanne. Using the Poisson distribution, we can calculate the probability of having four hurricanes in one year.

According to the USA Today, the probability of Tampa, Fla. experiencing a hurricane is 17.5%. Using the Poisson calculator, the mean (lambda) = .175. Leave the offset at zero. Since we want to know the odds of four hurricanes, then X = 4.

  • P(X=4) indicates that the probability of having four hurricanes in one year is .000032 or roughly 3 in 10,000.

  • P(X>=4) indicates that the probability of having fouror morehurricanes in one year is .000033.

  • The bar X=0 indicates the probability of having no hurricanes in a year.

  • The bar X=1 indicates the probability of having one hurricane in a year.

ProbHurricane

See Also