Theorem 3.2.1 / Corollary / Theorem 3.2.2: joint, marginal and
total-runs pmfs under randomness. Mirrors morie.fn.gb321/gb321c/
gb322.
Usage
morie_runs_pmf(n1, n2, r1 = NULL, r2 = NULL, r = NULL)
Arguments
- n1, n2
counts of the two element types.
- r1, r2
run counts for the joint pmf (optional).
- r
total runs for the total pmf (optional).
Value
list: joint (if r1, r2 given), marginal_r1 (vector over
r1 = 1..n1), total (vector over r = 2..n1+n2), mean, var.
References
Gibbons & Chakraborti (2021), Nonparametric
Statistical Inference, 5th ed., Theorems 3.2.1-3.2.2,
eqs. (3.2.6), (3.2.8).
Examples
morie_runs_pmf(4, 5)$mean
#> [1] 5.444444
