Arc-Length Statistics: Goodness of Fit, Distributions and a Bayesian Test

Inference from the arc length of statistical functions. Three tools share one pure-C back-end: a goodness-of-fit test based on the arc length of the probability plot, with an analytic saddlepoint null and sensitivity to local density structure that the empirical-distribution tests miss; two constructions that build a distribution from the arc length of its defining curve, the arc-length generator and the quantile arc-length family estimated by L-moments; and a Bayesian nonparametric arc-length goodness-of-fit test on the Dirichlet-process posterior. The same C sources back the 'Python' package 'arcstat'.

arcstat

Inference from the arc length of statistical functions: a goodness-of-fit test on the arc length of the probability plot, distributions built from the arc length of their defining curve, the characteristic-function version, the equivalence family, and a Bayesian test.

Computation runs on a shared pure-C back-end that is also bound from Python, and the two front ends are checked against each other value by value.

Installation

# install.packages("remotes")
remotes::install_github("mtloots/arcstat", subdir = "arcstat")

Usage

library(arcstat)
set.seed(1)
al_test(runif(200))$p.value
#> [1] 0.3974529

## two closed forms that anchor the construction
c(normal = cf_arclength_family("normal"),
  exponential = cf_arclength_family("exponential", lambda = 1))
#>      normal exponential 
#>    2.000000    3.141593