A Closed-Form Approximation to the Distribution for the Sum of Independent Non-identically Generalized Gamma Variates and Applications
Bibliographic record
Abstract
Evaluating the sum of independent and not necessarily identically distributed (i.n.i.d) random variables (RVs) is essential to study different variables linked to various scientific fields, particularly, in wireless communication channels. However, it is difficult to evaluate the distribution of this sum when the number of RVs increases. Consequently, the complex contour integral will be difficult to determine. Considering this issue, a more accurate approximation of the distribution function is required. By assuming the probability density function (PDF) of a generalized gamma (GG) RV evaluated in terms of a proper subset H1,0 1,1 class of Fox’s H-function (FHF) and the moment-based approximation to estimate the FHF parameters, a closed-form tight approximate expression for the distribution of the sum of i.n.i.d GG RVs and a sufficient condition for the convergence are investigated. The proposed approximate may be an analytical useful tool for analyzing the performance of certain numbers branch maximal-ratio combining receivers subject to GG fading channels. Hence, various closed-form performance metrics are derived and examined in terms of FHF. Numerical simulations are carried out to illustrate the theoretical results.
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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 | 0.003 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.002 |
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".