Our code goes through multiple stages of review. I wish to use the number of defects at an earlier stage of review as a "defect density" estimate for later stages.

It sometimes happens that code has zero defects in the early stage of review. This is causing me trouble since if $\lambda = 0$ then $P(k)=\frac{e^{-\lambda t}(\lambda t)^k}{k!}=0$ for all $k$.

R does indeed just throw an error in this case:

```
foo = 0:10
bar = 2 * foo
glm(bar ~ log(foo), family = poisson)
# fails because log(0) = -Inf
```

I could get around this in several ways:

- Ignore places with zeros (this would drop 1,486 of my 4,476 data points)
- Replace all the zeros with some number
- Add one to everything

What's the best way to handle this?

## Best Answer

Either (as mentioned in a comment by @Glen_b) use Bayesian methods, or some kind of

borrowing strength, that is, analyzing multiple data sets with a common model, with some common parameters (that can be seen as a way of empirical bayes.) You sayThe estimated (mle) parameter of zero leads to predictions of zero future errors, though one could make prediction intervals (of the form $[0, .)$) for number of future errors, in some model. But borrowing strength by modeling multiple datasets together seems to me better. This is now a deveoped field, see https://en.wikipedia.org/wiki/List_of_software_reliability_models and this google scholar search