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Goodness-of-fit test against a wrapped Cauchy distribution

Source: R/circular_statistics.R
test_gof.Rd

Tests whether each group's headings plausibly come from a wrapped Cauchy distribution, using Watson's U^2 statistic on the probability-integral transform of the fitted distribution, with a parametric-bootstrap p-value (the bootstrap accounts for the mean direction and concentration having been estimated from the same sample, which invalidates the naive tabled p-value for watson.test()). Unlike test_uniformity, which tests "is this uniform?", test_gof tests a different null hypothesis: "does this fit a wrapped Cauchy?" — useful when a unimodal but non-von-Mises shape (heavier or lighter tails) is suspected.

Usage

test_gof(
  hd,
  group_col = NULL,
  angle_col = "heading",
  dist = c("wrappedcauchy"),
  p_adjust = "none",
  n_boot = 999L
)

Arguments

hd

Data frame with a heading column in radians.

group_col

Column to group by. NULL tests the whole data frame as one group.

angle_col

Heading column name. Default "heading".

dist

Candidate distribution family. Currently only "wrappedcauchy" is implemented.

p_adjust

Multiple-comparison correction method passed to p.adjust. Default "none". Applies only when group_col is supplied; a p_value_adj column is added to the result.

n_boot

Number of parametric bootstrap replicates for the p-value. Default 999. Each replicate refits the wrapped-Cauchy MLE, so this is more expensive per-replicate than the package's other Monte-Carlo p-values; lower it for quick exploratory calls. Set the RNG seed with set.seed for reproducible p-values.

Value

Tidy data frame with columns group_col (if supplied), statistic, p_value, n, mu (fitted mean direction, radians), rho (fitted concentration, [0, 1)), test, and p_value_adj (when p_adjust != "none"). Returns NULL (ungrouped) or omits a group's row (grouped) when that sample has fewer than 3 finite angles or the fit fails to converge. If the wrapped-Cauchy fit succeeds but the bootstrap step itself fails, the row is kept with valid statistic/mu/rho but p_value set to NA.