forecasting-ch19-diffusionlisted

# Chapter 19: Frank Bass and the Television ## Scope and intake Use when first adoption of a durable product or category may follow diffusion with an uncertain ceiling. Do not use for forecasting recurring purchase units directly from a unique-adopter Bass curve. Ask only for unresolved material inputs: Does the series count cumulative unique adopters? What is the market ceiling’s evidence? Are time units consistent? Has the inflection or peak been observed? What repeat behavior lies outside adoption? ## Input contract and additional evidence Cumulative unique adopters at six or more increasing times, with `ceilings` naming at least one defended market ceiling above the observed total. `repeat_kernel` lists expected repeat units per original trier at cohort ages one, two, three and so on; `units_at_trial` is the first-purchase quantity. `parfitt_collins` takes `T` (eventual trial share), `R` (repeat share) and optional `B` (buying-rate index). Minimal **format illustration**, not sufficient training data: ```csv time,adopters 1,2944 2,6931 3,12179 4,18839 ``` ## Executable interface Exact CLI columns: `time,adopters`. Supported method controls: `as_of, ceilings, fix_q, frequency, future_times, horizon, parfitt_collins, peak, repeat_kernel, sales_horizon, season, seed, time_unit, units_at_trial`. The tool fits the Bass model for each declared ceiling (with early-fit holdout, Jacobian condition and peak time), optionally refits with `fix_q` held, then converts adoptio