Order-statistic laws: median, coverage, binomial-beta identity

Bundles the Ch. 2 exact results mirrored from gb_med/gb2111c/ gb2431/gb2311: the odd-n sample-median CDF I_F(m+1, m+1), the elementary-coverage law Beta(1, n), the binomial-tail = incomplete-beta identity, and the pointwise EDF moments.

Usage

morie_order_statistic_laws(n, F_x = NULL, t = NULL, r = NULL)

Arguments

n

sample size.

F_x

CDF value(s) for the median CDF / EDF moments.

t, r

arguments of the binomial-beta identity (optional).

Value

list: median_cdf (odd n only, else NULL), coverage_mean, coverage_var, edf_mean, edf_var, identity_lhs/rhs (if t, r given).

References

Gibbons & Chakraborti (2021), Chs. 2.3, 2.7.1, 2.11.1, Corollary 2.4.3.1.

Examples

morie_order_statistic_laws(11, F_x = 0.5)$median_cdf
#> [1] 0.5