Characterize and compare transfer-count distributions over time
Overview
This question evaluates a candidate's ability to model zero-inflated, heavy-tailed count data, interpret distributional summaries and percentiles, reason about temporal shifts from retention and fraud dynamics, and identify robust summary statistics and diagnostics for a Data Scientist role.
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Oct 13, 2025, 9:49 PM
Data Scientist
Onsite
Statistics & Math
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P2P Transfer Counts in First 30 Days: Distribution, Summaries, and Evolution
Context: For a new user cohort, define X as each user’s number of peer-to-peer (P2P) transfers completed in the first 30 days post-signup. X is a nonnegative integer count that often has many zeros (inactive users) and a heavy right tail (high-intensity users and potential abuse).
Tasks
- Propose a plausible distributional family for X (e.g., zero-inflated negative binomial, hurdle model, or a lognormal mixture). Justify both the expected mass at zero and heavy-tail behavior.
- Sketch the likely ordering and approximate locations of the mode, median, mean, and 95th percentile for X, and explain why they differ.
- Describe how this distribution should evolve by day 60 considering selection on retention, habit formation, fraud suppression, and seasonality. Predict directional shifts of the mode, median, mean, and 95th percentile.
- Recommend two robust, executive-level summaries resilient to heavy tails (e.g., trimmed mean, median-of-ratios) and one diagnostic (e.g., QQ plot or tail index) to validate assumptions.
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