Law of the iterated logarithm ratio and the Chung liminf constant

Kosorok eq. (2.21): \(\limsup \|G_n\|_\infty / \sqrt{2\log\log n} \le 1/2\) a.s., with Chung's companion \(\liminf \sqrt{2\log\log n}\|G_n\|_\infty = \pi/2\). Mirrors morie.fn.ksr058.

Usage

morie_lil_ratio(x, F = NULL)

Arguments

x

numeric sample.

F

optional CDF.

Value

list: sup_norm, lil_ratio, lil_bound (0.5), chung_liminf_constant (pi/2), loglog_term, n.

References

Kosorok (2008), eq. (2.21).

Examples

set.seed(1)
morie_lil_ratio(runif(1000))$lil_ratio
#> [1] 0.391912