On the existence and uniqueness of the maximum likelihood estimates of the parameters of Birnbaum–Saunders distribution based on Type-I, Type-II and hybrid censored samples
Bibliographic record
Abstract
The Birnbaum–Saunders (BS) distribution is a positively skewed distribution and is a common model for analysing lifetime data. In this paper, we discuss the existence and uniqueness of the maximum likelihood estimates (MLEs) of the parameters of BS distribution based on Type-I, Type-II and hybrid censored samples. The line of proof is based on the monotonicity property of the likelihood function. We then describe the numerical iterative procedure for determining the MLEs of the parameters, and point out briefly some recently developed simple methods of estimation in the case of Type-II censoring. Some graphical illustrations of the approach are given for three real data from the reliability literature. Finally, for illustrative purpose, we also present an example in which the MLEs do not exist.
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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 | 0.021 | 0.120 |
| 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 | 0.007 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".