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Eric Coissac
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- Update obioptions.Version from "Release 4.4.29" to "/v/ Release v5" - Update version.txt from 4.29 → .30 (automated by Makefile)
27 lines
1.8 KiB
Markdown
27 lines
1.8 KiB
Markdown
# `BetaKolmogorovDist` Function — Semantic Description
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The `obistats.BetaKolmogorovDist` function computes a **goodness-of-fit statistic** between an empirical dataset and the *cumulative distribution* (CDF) of a **Beta probability distribution** with specified parameters `α` and `β`. It implements an adapted version of the **Kolmogorov–Smirnov (KS) test**, tailored for Beta-distributed theoretical models.
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### Key Functionalities:
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- **Input**:
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- `data []float64`: Empirical sample (assumed sorted if `preordered = true`).
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- `alpha`, `beta float64`: Shape parameters of the target Beta distribution.
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- **Processing**:
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- If not pre-sorted, data is copied and sorted ascendingly.
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- For each ordered sample point `v_i`, it accumulates the sum `s = Σ_{j≤i} v_j`.
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- Evaluates:
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`|CDF_Beta(s; α, β) − empirical CDF_i|`, where the *empirical* cumulative probability at rank `i` is approximated as `1/(i+1)` — a common Bayesian/maximum-likelihood estimator (e.g., median-rank).
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- Returns the **supremum** of these absolute deviations (i.e., max distance across all points).
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### Interpretation:
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- A **small value** indicates the empirical cumulative sums align closely with the theoretical Beta CDF.
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- A **large value** suggests significant deviation — poor fit of aBeta(α,β) to the data.
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- Unlike standard KS tests (which use `i/n`), this uses `1/(i+1)` — suitable for small samples or Bayesian contexts.
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### Dependencies:
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- Uses `gonum.org/v1/gonum/stat/distuv.Beta` for CDF computation.
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- Uses `gonum.org/v1/gonum/floats.Max` for distance extremal computation.
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- `sort.Float64s` ensures ordered traversal.
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> **Note**: The use of *cumulative sums* (`s`) rather than raw values is unconventional — possibly intended for data representing proportions or waiting times where the *integral* of observations matters.
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