Confidence Interval Estimation for the Ratio of Binomial Proportions and Random Numbers Generation for Some Statistical Models
Bibliographic record
Abstract
A general problem of the interval estimation for a ratio of two proportions p1=p2 according to data from two independent samples is considered. Each sample may be obtained in the framework of direct or inverse binomial sampling. Asymptotic confidence intervals are constructed in accordance with different types of sampling schemes with an application, where it is possible, of unbiased estimations of success probabilities and also their logarithms. Since methods of constructing confidence intervals in the situations when values for the both samples are obtained for identical sample schemes are already developed and well known, the main purpose of this paper is the investigation of constructing confidence intervals in two cases that correspond to different sampling schemes. In this situation it is possible to plan the sample size for the second sample according to the number of successes in the first sample. This, as it is shown by the results of statistical modeling, provides the intervals with confidence level which closer to the nominal value. Next, we provide a new procedure to generate random number that follow three parameter Crack distribution. To generate Crack random number by composition method, first we generate random number from already known two parameter distributions: Inverse Gaussian distribution, and Length Biased Inverse Gaussian distribution. Finally, we derive Crack random number generation procedure. Note that for many years the temperature and its temporal and spatial dynamics have been one of the determinants of demographic processes. The use of temperature values measured at the centre of population could significantly increase the accuracy of birth vs. temperature correlation analysis. Within the reported studies we have determined the center of population of the province of Saskatchewan of Canada. Unavailability of western-laboratory-type data on water quality for the areas where the aboriginal people live requires developing special evaluation and prognosis-making methodologies. To determine the key parameters of the water quality we interviewed the experts (aboriginal elders). Basing on the determined key parameters we formed the key questions and developed the questionnaires. The questionnaires were distributed among the households of the Peepeekisis and Kahkewistahaw aboriginal communities (Saskatchewan, Canada).
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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 | 0.040 | 0.268 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.003 |
| Bibliometrics | 0.005 | 0.003 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.004 | 0.004 |
| Open science | 0.005 | 0.003 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.006 | 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".