Generates random samples from the rho = sum w_h^2 distribution by
stick-breaking simulation.
Usage
rrho(n, a, b, n_sticks = 500L)
Arguments
- n
Integer; number of samples to generate.
- a
Numeric; shape parameter of the Gamma prior on alpha (a > 0).
- b
Numeric; rate parameter of the Gamma prior on alpha (b > 0).
- n_sticks
Integer; number of sticks for truncation. Default is 500.
Value
Numeric vector of length n; random samples from the rho distribution.
Details
Uses the hierarchical representation:
alpha ~ Gamma(a, b)
v_h | alpha ~ Beta(1, alpha) independently for h = 1, ..., n_sticks
w_1 = v_1, w_h = v_h * prod(1 - v_l) for l < h
rho = sum w_h^2
Useful for Monte Carlo validation of analytical formulas.
See also
rw1 for w1 random generation
Examples
set.seed(42)
rho_samples <- rrho(1000, a = 2, b = 1)
mean(rho_samples)
#> [1] 0.4096141
mean_rho(a = 2, b = 1)
#> [1] 0.4036526
