Estimation of the Parameters in the Double-periodic Model
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Bibliographic record
Abstract
The periodic behavior of environmental conditions and its effects on waiting time is of principal interest in a number of modeling problems. Dimitrov and Khalil (1992) have used a constructive approach to introduce a new class of probability distributions which exhibits the periodic behavior of environmental conditions in time and the random occurrence of some events on each time period. Further, the authors discussed some physical and probabilistic properties of the new class. In a more recent work, Dimitrov et al. (1996) investigated a somewhat more complicated case of modeling the waiting time to occurrence of a random event governed by random environment with driving periodic or double periodic structure. In this contribution, we will make use of these important results to find estimators of the parameters in the double periodic model, where after a given number of time periods, say m, the conditions start to repeat, the same as from the origin. Phenomena of this type appear in a series of environmental, maintenance and financial processes. In particular, we expect that investigators working in modeling environmental evolution with periodic behavior will find our new results useful.
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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 | 0.001 | 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 | 0.000 |
| Open science | 0.002 | 0.001 |
| 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 it