{"ID":2889154,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.21712","arxiv_id":"2507.21712","title":"An Equal-Probability Partition of the Sample Space: A Non-parametric Inference from Finite Samples","abstract":"This paper investigates what can be inferred about an arbitrary continuous probability distribution from a finite sample of $N$ observations drawn from it. The central finding is that the $N$ sorted sample points partition the real line into $N+1$ segments, each carrying an expected probability mass of exactly $1/(N+1)$. This non-parametric result, which follows from fundamental properties of order statistics, holds regardless of the underlying distribution's shape. This equal-probability partition yields a discrete entropy of $\\log_2(N+1)$ bits, which quantifies the information gained from the sample and contrasts with Shannon's results for continuous variables. I compare this partition-based framework to the conventional ECDF and discuss its implications for robust non-parametric inference, particularly in density and tail estimation.","short_abstract":"This paper investigates what can be inferred about an arbitrary continuous probability distribution from a finite sample of $N$ observations drawn from it. The central finding is that the $N$ sorted sample points partition the real line into $N+1$ segments, each carrying an expected probability mass of exactly $1/(N+1)...","url_abs":"https://arxiv.org/abs/2507.21712","url_pdf":"https://arxiv.org/pdf/2507.21712v1","authors":"[\"Urban Eriksson\"]","published":"2025-07-29T11:39:13Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\",\"stat.ME\"]","methods":"[]","has_code":false}