A Review of the Methodologies Used in the Derivation of Formulas for Parametric Survival Functions with Illustrative Numerical Examples
Bibliographic record
Abstract
In this review paper formulas for survival functions are derived that take into account risks of deaths in early life including infancy, mid life, a random component of deaths due to accidents and deaths in older ages. The basic ideas used in the derivation of survival function for each of the components just mentioned are risk functions. Given a formula for a risk function, it is possible to derive a formula for the corresponding survival function. By using the theory of competing risks, a formula for survival function that takes into account the risks of deaths in various stages of life expressed as a product of survival functions for the risks of deaths under consideration. For many applications information on the numerical values of parameters in survival functions is not available. Consequently, rationales are developed for assigning plausible values to parameters that take into account personal ideas of an investigator may have for each stage of life. For every assignment of parameter values in the paper, a numerical version of survival functions are plotted in graphs so that an assessment of the plausibility of the chosen parameter values may be made. Also included in the paper is an application of survival functions in an experiment to make an assessment as to whether a small population of chimpanzees, or some other endangered species of animals, will have descendants that make up a surviving population 200 years into the future.
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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 | 0.003 | 0.012 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.006 | 0.008 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.008 | 0.007 |
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".