PiecewisePareto_Layer_Var {Pareto}

Layer Variance of the Piecewise Pareto Distribution

Description

Calculate the variance of a piecewise Pareto distribution in a reinsurance layer

Usage

PiecewisePareto_Layer_Var(
  Cover,
  AttachmentPoint,
  t,
  alpha,
  truncation = NULL,
  truncation_type = "lp"
)

Arguments

Cover

Numeric. Cover of the reinsurance layer.

AttachmentPoint

Numeric. Attachment point of the reinsurance layer.

t

Numeric vector. Thresholds of the piecewise Pareto distribution.

alpha

Numeric vector. alpha[i] is the Pareto alpha in excess of t[i].

truncation

Numeric. If truncation is not NULL and truncation > t, then the Pareto distribution is truncated at truncation.

truncation_type

Character. If truncation_type = "wd" then the whole distribution is truncated. If truncation_type = "lp" then a truncated Pareto is used for the last piece.

Value

The variance of the (truncated) piecewise Pareto distribution with parameter vectors t and alpha in the layer Cover xs AttachmentPoint

Examples

t <- c(1000, 2000, 3000)
alpha <- c(1, 1.5, 2)
PiecewisePareto_Layer_Var(4000, 1000, t, alpha)
PiecewisePareto_Layer_SM(4000, 1000, t, alpha) - PiecewisePareto_Layer_Mean(4000, 1000, t, alpha)^2
PiecewisePareto_Layer_Var(4000, 1000, t, alpha, truncation = 5000)
PiecewisePareto_Layer_Var(4000, 1000, t, alpha, truncation = 5000, truncation_type = "lp")
PiecewisePareto_Layer_Var(4000, 1000, t, alpha, truncation = 5000, truncation_type = "wd")