# Fitting Poisson Distribution to Data: Need Help!

• timmyc
In summary, The person needs help fitting a Poisson distribution to a set of data consisting of 500 counts of radioactive decay, with the counts ranging from 0 to 9. They have calculated the mean and variance to be 67.1, but are having trouble using this in the formula without getting a math error. Another person suggests that the mean should be around 2+ based on the given data.

#### timmyc

I need to fit a Poisson distribution to this set of data (no. of counts of radioactive decay)

The number of counts in a fixed time interval was recorded 500 times.

With the number of counts going from 0 - 9 respectively

39
106
130
100
67
34
15
7
1
1

I understand how to use the formula in simple probability situations but am a little stuck with this one.

I know the mean = the variance and worked that out to be 67.1 but when using this in the formlua I calculated explodes (shows math error).

How did you get 67.1? Off hand (without doing the arithmetic) the mean looks like it should be around 2+.

(39x0 + 106x1 + 130x2 + ... + 1x9)/500

## 1. What is a Poisson distribution?

A Poisson distribution is a statistical distribution that is used to model the number of times an event occurs within a specific time or space, given the average rate of occurrence and assuming that each event is independent of the others.

## 2. How do you fit a Poisson distribution to data?

To fit a Poisson distribution to data, you need to first calculate the mean and variance of the data. Then, you can use the Poisson formula to calculate the probability of each value occurring. Finally, you can compare these probabilities to the actual data and adjust the parameters of the Poisson distribution until you find the best fit.

## 3. What types of data are suitable for fitting a Poisson distribution?

Poisson distributions are commonly used to model count data, such as the number of customers entering a store, the number of accidents in a certain time period, or the number of emails received per day. The data should also have a finite range and each event should be independent of the others.

## 4. What are the limitations of using a Poisson distribution to model data?

Poisson distributions assume that the mean and variance of the data are equal, which may not be the case in real-world scenarios. They also assume that each event is independent, which may not be true for some types of data. Additionally, Poisson distributions are only suitable for data with a finite range.

## 5. How do you determine if a Poisson distribution is a good fit for your data?

You can determine if a Poisson distribution is a good fit for your data by visually comparing the distribution of the data to the Poisson curve. You can also use statistical tests, such as the chi-square test, to assess the goodness of fit. Additionally, you can check if the mean and variance of the data are approximately equal, which is a requirement for a Poisson distribution.