Parameter estimation for reduced Type-I Heavy-Tailed Weibull distribution under progressive Type-II censoring scheme
Bibliographic record
Abstract
Reduced Type-I heavy-tailed Weibull (RTI-HTW) distribution is a particular case of the Type-I heavy-tailed family of distributions. This article has studied the properties, inference and real-life applications of RTI-HTW distribution. Firstly, properties such as quantile function, moment-generating function, stress–strength reliability, measure of uncertainty, and mean residual life have been discussed. Further, the inference of RTI-HTW distribution has been discussed under classical and Bayesian frameworks. We have studied the point and interval estimations of model parameters under the progressive Type-II censoring scheme. Four point estimation methods have been used to find the point estimates, such as maximum likelihood estimate (MLE), improved MLE, and Bayesian estimates under informative and kernel priors. Additionally, the approximate confidence interval has been calculated using MLEs, whereas the credible interval has been derived using the Bayesian estimates under informative prior. A Monte Carlo simulation study has been discussed to compare the results of all methods. To illustrate the practical applicability of the proposed model and methodologies, we have analyzed two real-world data sets: the mortality rate of COVID-19 patients in Canada and the infant mortality rate in China. Numerical results demonstrate that the proposed model provides a good fit for both data sets, and the estimation methods discussed are effective and satisfactory.
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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 | 0.008 | 0.021 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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".