Survival function and layer variance

survival(dist, q) is P(X > q), accurate far into the tail; layer_variance(dist, limit, attachment) is the variance of the loss to the layer limit xs attachment (Inf for an unlimited layer). Defined for the Pareto-family severities (pareto, piecewise_pareto, log_affine_pareto, generalized_pareto) and for gamma_distribution, tweedie, weibull_distribution, loglogistic_distribution, mixture_distribution and custom_distribution.

Usage

survival(dist, q, ...)

layer_variance(dist, limit, attachment, ...)

Arguments

dist

A Pareto-family severity.

q

Numeric vector.

...

Unused; for methods.

limit

Layer limit, a single number.

attachment

Layer attachment, a single number.

Value

A numeric vector (survival) or a single number (layer_variance).

Examples

p <- pareto(500, 2)
survival(p, c(1000, 2000))
#> [1] 0.2500 0.0625
layer_variance(p, 4000, 1000)
#> [1] 364719