New Logistic Family of Distributions: Applications to Reliability Engineering
Bibliographic record
Abstract
This study introduces a novel family of probability distributions, termed the Pi-Power Logistic-G family, constructed through the application of the Pi-power transformation technique. By employing the Weibull distribution as the baseline generator, a new and flexible model, the Pi-Power Logistic Weibull distribution, is formulated. Particular emphasis is given to this specific member of the family, which demonstrates a rich variety of hazard rate shapes, including J-shaped, reverse J-shaped, and monotonic increasing patterns, thereby highlighting its adaptability in modeling diverse types of lifetime data. The paper examines the fundamental properties of this distribution and applies the method of maximum likelihood estimation (MLE) to determine its parameters. A Monte Carlo simulation was performed to assess the performance of the estimation method, demonstrating that both Bias and mean square error decline as the sample size increases. The utility of the proposed distribution is further highlighted through its application to real-world engineering datasets. Using model selection metrics and goodness-of-fit tests, the results demonstrate that the proposed model outperforms existing alternatives. In addition, a Bayesian approach was used to estimate the parameters of both datasets, further extending the model’s applicability. The findings of this study have significant implications for the fields of reliability modeling, survival analysis, and distribution theory, enhancing methodologies and offering valuable theoretical insights.
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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 | 0.005 | 0.022 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".