Simulate positive bulk-tail data

Generate synthetic outcomes with a light-to-moderate bulk and a heavier upper tail. The sample is assembled from a lognormal-gamma bulk and a shifted tail sample, then sorted. This generator is intended for examples, help pages, and workflow checks rather than as a formal generative model matching the full package hierarchy exactly.

Usage

sim_bulk_tail(n = 200, tail_prob = 0.12, seed = NULL)

Arguments

n

Integer sample size.

tail_prob

Approximate tail probability \(\Pr(X > u)\) used to split the sample into bulk and tail draws.

seed

Optional random seed for reproducibility.

Value

Numeric vector of length n containing positive outcomes sorted in ascending order.

Details

The generator approximates a spliced sample $$ X \sim (1 - \pi_u) F_{bulk} + \pi_u F_{tail}, $$ where \(\pi_u =\) tail_prob. The bulk component is itself a simple two-component mixture, while the tail component is a shifted positive distribution that produces larger values.

Use this helper when you need a fast toy sample for bundle(), dpmix(), or dpmgpd(). It should not be interpreted as posterior predictive simulation from a fitted object.

See also

sim_causal_qte(), sim_survival_tail(), bundle(), dpmgpd().

Other simulation helpers: sim_causal_qte(), sim_survival_tail()