I went straight to Poisson because that's the reflex answer for count data, but they pushed back pretty fast.
Start by clarifying the context: unique recipients per caller is a count of distinct contacts, likely over a fixed time window. Then propose a distribution like Negative Binomial or Poisson, justifying based on overdispersion and the nature of contact behavior. Finally, outline a validation plan using goodness-of-fit tests, visual diagnostics, and out-of-sample checks.
Pro tip: Mention that in practice, you'd also consider zero-inflation or mixture models if many callers have zero or few recipients, and that validating with business metrics (e.g., prediction error on holdout) matters more than pure statistical fit.
Define what 'unique recipients' means (e.g., distinct phone numbers contacted) and the time window (daily, weekly). Consider if the count is per caller and whether there are structural zeros (callers who contact no one).
Propose Poisson if mean≈variance, but likely Negative Binomial due to overdispersion from heterogeneity in caller behavior. Mention alternatives like Zero-Inflated Poisson/Negative Binomial if many zeros.
Use goodness-of-fit tests (chi-square, Kolmogorov-Smirnov), compare AIC/BIC, and check dispersion statistics. Plot observed vs. expected frequencies and QQ plots.
Split data into train/test, fit on train, and evaluate predictive performance on test (e.g., log-likelihood, MAE). Check if the model captures key business patterns (e.g., heavy tail).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.