# Fit_PML_Curve: Fits a Collective Model to a PML Curve In Pareto: The Pareto, Piecewise Pareto and Generalized Pareto Distribution

 Fit_PML_Curve R Documentation

## Fits a Collective Model to a PML Curve

### Description

Fits a PPP_Model that matches the values of a PML curve

### Usage

``````Fit_PML_Curve(
return_periods,
amounts,
tail_alpha = 2,
truncation = NULL,
truncation_type = "lp",
dispersion = 1
)
``````

### Arguments

 `return_periods` Numeric vector. Vector containing the return periods of the PML curve. `amounts` Numeric vector. Vector containing the loss amounts corresponding to the return periods. `tail_alpha` Numerical. Pareto alpha that is used above the highest amount of the PML curve. `truncation` Numeric. If `truncation` is not `NULL` and `truncation > max(t)`, then the 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. `dispersion` Numerical. Dispersion of the claim count distribution in the resulting PPP_Model.

### Value

A PPP_Model object that contains the information about a collective model with a Panjer distributed claim count and a Piecewise Pareto distributed severity. The object contains the following elements:

• `FQ` Numerical. Frequency in excess of the lowest threshold of the piecewise Pareto distribution

• `t` Numeric vector. Vector containing the thresholds for the piecewise Pareto distribution

• `alpha` Numeric vector. Vector containing the Pareto alphas of the piecewise Pareto distribution

• `truncation` Numerical. If `truncation` is not `NULL` and `truncation > max(t)`, then the 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.

• `dispersion` Numerical. Dispersion of the Panjer distribution (i.e. variance to mean ratio).

• `Status` Numerical indicator: 0 = success, 1 = some information has been ignored, 2 = no solution found

• `Comment` Character. Information on whether the fit was successful

### Examples

``````return_periods <- c(1, 5, 10, 20, 50, 100)
amounts <- c(1000, 4000, 7000, 10000, 13000, 14000)

fit <- Fit_PML_Curve(return_periods, amounts)
1 / Excess_Frequency(fit, amounts)

fit <- Fit_PML_Curve(return_periods, amounts, tail_alpha = 1.5,
truncation = 20000, truncation_type = "wd")
1 / Excess_Frequency(fit, amounts)

``````

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