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Asymptotic relative efficiencies of the classical location tests

Source: R/gibbons_native.R
morie_are_nonparametric.Rd

Table 13.3.1 (PDF-verified, printed p. 492) plus the efficacy integrals re-deriving it from the density, the Hodges-Lehmann bounds, and the scale-test values of Sec. 13.3.3. Mirrors the morie.fn gb_are*/gb_ar* family.

Usage

morie_are_nonparametric(distribution = "normal")

Arguments

distribution

"uniform", "normal", "logistic" or "double_exponential".

Value

list: wilcoxon_vs_t, sign_vs_t, sign_vs_wilcoxon, derived (same three from numerical integration), hl_bound_wilcoxon (0.864), are_mood_f, are_klotz_f.

Details

NOTE the Mood value: ARE(Mood, F | normal) = 15/(2 pi^2) = 0.760 (the book's own e(M_N) derivation), not the 3/pi a placeholder once claimed.

References

Gibbons & Chakraborti (2021), Table 13.3.1, Sec. 13.3.3. Hodges & Lehmann (1956), Ann. Math. Statist. 27(2), 324-335.

Examples

morie_are_nonparametric("normal")$wilcoxon_vs_t
#> [1] 0.9549297