Model Unique Recipients with Poisson Distribution and Test Fit

Q: Model Unique Recipients with Poisson Distribution and Test Fit

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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Question

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.

Model Unique Recipients with Poisson Distribution and Test Fit

Modeling Unique Recipients per Caller

Scenario

Question

Guidance

Solution

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