Approximation of the lognormal distribution as a solution to the sum of lognormal variates
Bibliographic record
Abstract
Lognormal distribution is widely used in modeling of variety fields such as fields of sciences and technology, human medicines, linguistics, social sciences and economics and others. In this research projects, three types of approximations, namely Wilkinson approximation, Schwartz and Yeh approximation and Inverse approximation are introduced to determine which approximations worked with the sum of empirical lognormal distributions and approximating its parameter values which will be generated using computational statistics. Throughout the method of computational statistics, the lognormal variates (Xi) will be generated empirically using normal simulation and Monte Carlo simulation by considering variety of simulation conditions such as the number of lognormal variates in the sum, the number of sample size in the variates, independent assumption, identically distributed assumption and non-identically distributed assumption for the lognormal variates. Anderson–Darling goodness of fit test is used to test and determine the best approximation among the three types of approximations. At the end of this research, the best approximation between Wilkinson approximation, Schwartz and Yeh approximation, and Inverse approximation based on the Type I Error rate and the complexness of the approximation’s method by considering the number of computational steps and total number of times needed for the analysis is determined.
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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 | 0.000 |
| 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 | 0.001 | 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".