Single-parameter Pareto distribution

P(X > x) = (t / x)^alpha for x >= t, optionally truncated (conditioned on X < truncation). Parameters are read-only properties: d@t, d@alpha, d@truncation (Inf if none).

Usage

pareto(t, alpha, truncation = NULL, ptr = NULL)

Arguments

t

Threshold; finite and positive.

alpha

Pareto alpha; finite and positive.

truncation

Truncation point above t, or NULL for none.

Value

A pareto object, which inherits from distribution.

Details

Supports mean(), variance(), stats::quantile(), cdf(), survival(), draws(), lev(), stop_loss(), layer(), layer_variance() and print(), and can be discretized with discretize() or used in simulate_events().

See also

pareto_fit() to estimate alpha from large losses.

Examples

p <- pareto(500, 2)
layer(p, 4000, 1000)
#> [1] 200
mean(p)
#> [1] 1000
pareto(500, 2, truncation = 8000)
#> <pareto> t = 500, alpha = 2, truncation = 8000