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 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 | 0.006 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".