# Poisson Distribution Analysis
Analyze rare event counts (defects, arrivals, incidents).
```console
$ lawkit poisson tests/fixtures/poisson_data.txt
Poisson Distribution Analysis Results
Dataset: tests/fixtures/poisson_data.txt
Numbers analyzed: 100
Quality Level: High
Probability Distribution:
P(X= 0): ██████████████████┃░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ 0.095
P(X= 1): ███████████████████████████████████████████┃░░░░░░ 0.224
P(X= 2): █████████████████████████████████████████████████┃ 0.263
...
λ=2.35, Variance/Mean=1.02 (ideal: 1.0), Fit Score=0.95
```
## Expected Lambda
```console
$ lawkit poisson tests/fixtures/poisson_data.txt --lambda 2.0
...
Expected λ: 2.0, Observed λ: 2.35
Deviation: 17.5%
```