# GenPareto_Layer_SM: Second Layer Moment of the Generalized Pareto Distribution In Pareto: The Pareto, Piecewise Pareto and Generalized Pareto Distribution

 GenPareto_Layer_SM R Documentation

## Second Layer Moment of the Generalized Pareto Distribution

### Description

Calculates the second moment of a generalized Pareto distribution in a reinsurance layer

### Usage

``````GenPareto_Layer_SM(
Cover,
AttachmentPoint,
t,
alpha_ini,
alpha_tail,
truncation = NULL
)
``````

### Arguments

 `Cover` Numeric. Cover of the reinsurance layer. Use `Inf` for unlimited layers. `AttachmentPoint` Numeric. Attachment point of the reinsurance layer. `t` Numeric. Threshold of the Pareto distribution. If `t` is `NULL` (default) then `t <- Attachment Point` is used `alpha_ini` Numeric. Initial Pareto alpha (at `t`). `alpha_tail` Numeric. Tail Pareto alpha. `truncation` Numeric. If `truncation` is not `NULL` and `truncation > t`, then the Pareto distribution is truncated at `truncation`.

### Value

The second moment of the (truncated) generalized Pareto distribution with parameters `t`, `alpha_ini` and `alpha_tail` in the layer `Cover` xs `AttachmentPoint`

### Examples

``````GenPareto_Layer_SM(4000, 1000, 1000, 1, 2)
GenPareto_Layer_SM(4000, 1000, t = 1000, alpha_ini = 1, alpha_tail = 3)
GenPareto_Layer_SM(4000, 1000, t = 5000, alpha_ini = 1, alpha_tail = 3)
GenPareto_Layer_SM(4000, 1000, t = 1000, alpha_ini = 1, alpha_tail = 3, truncation = 5000)
GenPareto_Layer_SM(9000, 1000, t = 1000, alpha_ini = 1, alpha_tail = 3, truncation = 5000)

``````

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