Dead Reckoning Counting Your Customers Who Never Say Goodbye
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摘要
This paper demonstrates that P(alive) in Buy-Till-You-Die models is the infinite-horizon limit of an observable finite-horizon forecast family, making the reported alive-based customer counts partially identified and highly sensitive to estimation conventions. Across a seven-year panel with 31,683 customers, interchangeable model specifications yield alive counts from 3,654 to 27,734 (7.6x spread); a software-default ridge penalty shifts counts by about 42%. Five years of subsequent purchases falsify the maximum-likelihood counts; the canonical CDNOW dataset shows a 2.4x spread. The category error—summing P(alive) versus horizon returns—accounts for most miscalibration. The remedy is to report a calibrated horizon count NH, maintain a dynamic calibration layer, audit across horizons and vintages, and report N∞ as an interval rather than a single point [page::2][page::4][page::16][page::19][page::15][page::23][page::25].
