New Modified Univariate Lindley Distribution: Statistical Properties, Estimation, and Applications
Bibliographic record
Abstract
This article centers on the exploration of a new univariate probability distribution. A novel distribution has been formulated using the power transformation technique, termed the new modified univariate Lindley distribution. This model exhibits diverse hazard functions, including J-shaped, reverse-J-shaped, and monotonically increasing patterns. The study examines the fundamental statistical characteristics of this recently introduced distribution, including moments, incomplete moments, hazard rate, mean residual life function, quantile function, skewness, and kurtosis. Estimation of its parameters is conducted through the maximum likelihood estimation method. The precision of this parameter estimation process is verified through Monte Carlo simulation experiments. To illustrate the practical utility of the proposed distribution, two sets of real-world data are employed. The performance of the suggested distribution model is assessed using various model selection criteria and goodness-of-fit test statistics. Empirical findings from these evaluations provide substantial evidence that the proposed model surpasses other existing models.
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How this classification was reachedexpand
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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".