Model Unique Recipients with Poisson Distribution and Test Fit
Overview
This question evaluates understanding of count-data modeling and statistical goodness-of-fit assessment, focusing on distributional assumptions for modeling the number of unique recipients per caller.
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Jul 12, 2025, 6:59 PM
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Modeling Unique Recipients per Caller
Scenario
You need to model the distribution of the count of unique recipients each caller contacts in a fixed time window. The goal is to use this model for capacity and growth planning (e.g., forecasting server load, messaging throughput, storage).
Question
Which statistical distribution would you use to model the number of recipients per caller, and how would you test the goodness-of-fit?
Guidance
- Consider common count distributions: Poisson, Binomial, Negative Binomial (and variants).
- Check dispersion (mean vs variance) and the presence of excess zeros.
- Fit via maximum likelihood.
- Validate with AIC/BIC, Pearson/Deviance goodness-of-fit, chi-square tests for discrete counts, discrete KS or simulation-based checks.
Solution
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