Derivation of a Closed-Form Asymptotic Variance for the Coefficient of Variation Under the Reparameterized Birnbaum–Saunders Distribution
Bibliographic record
Abstract
This study develops a tractable, closed-form expression for the asymptotic variance of the coefficient of variation (CV) estimator under a reparameterized Birnbaum–Saunders (BirSau) distribution. Using the method of moments, we derive analytical formulas for the mean, variance, and coefficient of variation of X∼BirSau(μ,λ) and construct a plug-in estimator for the CV. By applying the delta method within this new nonlinear parametrization, we obtain an explicit and compact expression for the asymptotic variance of the CV estimator, thereby extending general asymptotic theory to a distribution-specific setting where higher-order moments lack closed forms under the classical parametrization. Extensive Monte Carlo simulations are conducted to examine the estimator’s finite-sample performance under various parameter configurations and sample sizes. The results demonstrate that the estimator exhibits decreasing bias and variance as the sample size increases, with strong convergence to its theoretical asymptotic behavior. A real-data application using rainfall measurements from northeastern Thailand further illustrates the practical utility of the proposed approach in quantifying relative variability across regions. These findings provide a concise analytical foundation for the coefficient of variation under the Birnbaum–Saunders framework, enhancing its theoretical development and facilitating practical implementation in environmental and reliability analyses.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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".