# PiecewisePareto_Layer_Var: Layer Variance of the Piecewise Pareto Distribution In Pareto: The Pareto, Piecewise Pareto and Generalized Pareto Distribution

 PiecewisePareto_Layer_Var R Documentation

## 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")

``````

Pareto documentation built on April 18, 2023, 9:10 a.m.