The New Bivariate Conway-Maxwell-Poisson Distribution Obtained by the Crossing Method
Bibliographic record
Abstract
Kimberly et al. had proposed in 2016 a bivariate function as a bivariate Conway-Maxwell-Poisson distribution (COM-Poisson) using the generalized bivariate Poisson distribution and the probability generating functions of the follow distributions: bivariate bernoulli, bivariate Poisson, bivariate geometric and bivariate binomial. By examining this paper we have shown that this bivariate function is constant and it double series is divergent, when it should have been 1. To overcome this deadlock, we propose a new bivariate Conway-Maxwell-Poisson distribution which is definetely a probability distribution based on the crossing method, method highlighted by Elion et al. in 2016 and revisited by Batsindila et al. and Mandangui et al. in 2019. And this is the purpose of this paper. To this bivariate distribution is attached two generalized linear models (GLM) whose resolution allows us to highlight, not only the independence between the variables forming the couple, but also the effect of the factors (or predictors) on these variables. The resulting correlation is negative, zero or positive depending on the values of a parameter; in particular for the bivariate Poisson distribution according to Berkhout and Plug. A simulation of data will be given at the end of the article to illustrate the model.
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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 | 0.005 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.008 | 0.002 |
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".