Modeling Sales of Multigeneration Technology Products in the Presence of Frequent Repeat Purchases: A Fractional Calculus-Based Approach
Why this work is in the frame
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Bibliographic record
Abstract
Frequently releasing a new product generation has become a common practice to sustain sales over time, thus accurately forecasting the sales trajectory of each product generation plays a vital role in the short-, medium-, and long-term planning of a firm. Classic multigeneration diffusion models do not incorporate within-generation repeat purchases, making them unusable for product lines with high rates of such purchases. Concentrating on technology products, we develop a multigeneration sales model to fill this void. We demonstrate that the new model can be used for predictive and prescriptive analytics. Our empirical results show that the new model estimates and forecasts sales more accurately than a state-of-the-art benchmark model that does not account for within-generation repeat purchases, underscoring the importance of incorporating repeat purchases. Furthermore, we use two different versions of our model to examine market entry timing under two main strategies, that is, (i) a phase-out transition strategy in which firms continue to sell the old generation after the release of the new generation, and (ii) a total transition strategy in which firms discontinue the old generation after the introduction of the new generation. Our results indicate that the repeat purchases rate determines whether it is optimal to expedite or delay the new product launch, underscoring the importance of incorporating repeat purchases in market entry strategies.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it