Fitting a Poisson Distribution
Fitting a Poisson Distribution involves finding the best match between observed data and the Poisson model. It is like searching for a hat that fits just right. Suppose, there is data on how often something happens, like the number of customers arriving at a store each hour. If this data follows a pattern where events are rare and occur independently, the Poisson distribution might be a good fit. To fit it, one compares the actual data to what the Poisson model predicts. If they match up well, it suggests that the Poisson distribution accurately describes the situation. In practical terms, fitting a Poisson Distribution helps in understanding and making predictions about situations involving rare events, like customer arrivals or machine failures. It is a bit like finding the right puzzle piece that fits snugly into the data available.
Example:
A sample of 200 similar firms in a big industrial town revealed the following distribution of fatal accidents in a year. Fit a Poisson distribution corresponding to it.
No. of Accidents | 0 | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|---|
No. of Firms | 91 | 69 | 33 | 4 | 2 | 1 |
Solution:
No. of Accidents (x) | No. of Firms (f) | fx | P(x) | Expected Frequencies |
---|---|---|---|---|
0 | 91 | 0 | 0.4493 | 89.9 |
1 | 69 | 69 | 0.3595 | 71.9 |
2 | 33 | 66 | 0.1438 | 28.7 |
3 | 4 | 12 | 0.0383 | 7.66 |
4 | 2 | 8 | 0.0077 | 1.54 |
5 | 1 | 5 | 0.0012 | 0.24 |
Total | 200 | 160 |
| 199.94 ~ 200 |
*Mean () =
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