On the Normal Approximations to the Method of Moments Point Estimators of the Parameter and Mean of the Zero-Truncated Poisson Distribution
Bibliographic record
Abstract
Abstract In applied statistical research, a common type of dataset used is count data. However, there are cases where zero events are not observed in the dataset. Consequently, the Poisson distribution, a basic discrete probability model, is inappropriate in such situations. Instead, we need to consider the so-called Zero-Truncated Poisson distribution. Unfortunately, deriving the simplest Method of Moments estimators for the parameter and mean of this distribution in closed form is not feasible. Therefore, estimating the Zero-Truncated Poisson parameter and mean becomes a challenging problem. In this article, the authors used the classical delta method to apply an estimation procedure for the zero-truncated Poisson parameter and the mean and investigated their asymptotic normality. Furthermore, we demonstrated the practicality of our approach through an application to a real-life dataset on unrest events in the southern border area of Thailand.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.017 | 0.064 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".