obitools4/autodoc/docmd/pkg/obistats/kolmogorovbeta.md

BetaKolmogorovDist Function — Semantic Description

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.

Key Functionalities:

• Input:
  • data []float64: Empirical sample (assumed sorted if preordered = true).
  • alpha, beta float64: Shape parameters of the target Beta distribution.
• Processing:
  • If not pre-sorted, data is copied and sorted ascendingly.
  • For each ordered sample point v_i, it accumulates the sum s = Σ_{j≤i} v_j.
  • Evaluates:
    |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).
  • Returns the supremum of these absolute deviations (i.e., max distance across all points).

Interpretation:

• A small value indicates the empirical cumulative sums align closely with the theoretical Beta CDF.
• A large value suggests significant deviation — poor fit of aBeta(α,β) to the data.
• Unlike standard KS tests (which use i/n), this uses 1/(i+1) — suitable for small samples or Bayesian contexts.

Dependencies:

• Uses gonum.org/v1/gonum/stat/distuv.Beta for CDF computation.
• Uses gonum.org/v1/gonum/floats.Max for distance extremal computation.
• sort.Float64s ensures ordered traversal.

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.