Modelling of Loan Non-Payments with Count Distributions Arising from Non-Exponential Inter-Arrival Times
Bibliographic record
Abstract
The number of non-payments is an indicator of delinquent behaviour in credit scoring, hence its estimation and prediction are of interest. The modelling of the number of non-payments, as count data, can be examined as a renewal process. In a renewal process, the number of events (such as non-payments) which has occurred up to a fixed time t is intimately connected with the inter-arrival times between the events. In the context of non-payments, the inter-arrival times correspond to the time between two subsequent non-payments. The probability mass function and the renewal function of the count distribution are often complicated, with terms involving factorial and gamma functions, and thus their computation may encounter numerical difficulties. In this paper, with the motivation of modelling the number of non-payments through a renewal process, a general method for computing the probabilities and the renewal function based on numerical Laplace transform inversion is discussed. This method is applied to some count distributions which are derived given the distributions of the inter-arrival times. Parameter estimation with maximum likelihood estimation is considered, with an application to a data set on number of non-payments from the literature.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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 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".