Exact null distribution of runs up and down

Enumeration over all n! orderings (n <= 9), mirroring morie.fn.gb32lu; moments (2n-1)/3 and (16n-29)/90 from Ch. 3.4 (gb34mn) are returned for comparison.

Usage

morie_runs_updown(n = NULL, x = NULL)

Arguments

n

sequence length, 3..9.

x

optional observed sequence of distinct values to score.

Value

list: support, pmf, mean, var, mean_formula, var_formula, observed, p_le, p_ge.

References

Gibbons & Chakraborti (2021), Ch. 3.4.

Examples

morie_runs_updown(n = 5)$mean
#> [1] 3