The Double Pareto-Lognormal Distribution—A New Parametric Model for Size Distributions
Bibliographic record
Abstract
A family of probability densities, which has proved useful in modelling the size distributions of various phenomens, including incomes and earnings, human settlement sizes, oil-field volumes and particle sizes, is introduced. The distribution, named herein as the double Pareto-lognormal or dPlN distribution, arises as that of the state of a geometric Brownian motion (GBM), with lognormally distributed initial state, after an exponentially distributed length of time (or equivalently as the distribution of the killed state of such a GBM with constant killing rate). A number of phenomena can be viewed as resulting from such a process (e.g., incomes, settlement sizes), which explains the good fit. Properties of the distribution are derived and estimation methods discussed. The distribution exhibits Paretian power-law) behaviour in both tails, and when plotted on logarithmic axes, its density exhibits hyperbolic-type behaviour.
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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 | 0.019 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.004 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 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".