# Local_Pareto_Alpha: Local Pareto Alpha In Pareto: The Pareto, Piecewise Pareto and Generalized Pareto Distribution

## Description

Calculates the local Pareto alpha of the normal, lognormal and gamma distribution

## Usage

 `1` ```Local_Pareto_Alpha(x, distribution, ...) ```

## Arguments

 `x` Numeric. Vector of thresholds at which the local Pareto alpha is calculated. `distribution` Character. `'lnorm'` for lognormal distribution (arguments: `meanlog`, `sdlog`) `'norm'` for normal distribution (arguments: `mean`, `sd`) `'gamma'` for gamma distribution (arguments: `shape`, `rate`, `scale`) `'weibull'` for weibull distribution (arguments: `shape`, `scale`) `'exp'` for exponential distribution (arguments: `rate`) `'Pareto'` for Pareto distribution (arguments: `t`, `alpha`, `truncation = NULL`) `'GenPareto'` for exp distribution (arguments: `t`, `alpha_ini`, `alpha_tail`, `truncation = NULL`) `'PiecewisePareto'` for exp distribution (arguments: `t`, `alpha`, `truncation = NULL`, `truncation_type = 'lp'`) `...` Arguments for the selected distribution

## Value

Local Pareto alpha of the selected distribution at `x`

## References

Riegel, U. (2008) Generalizations of common ILF models. Blaetter der DGVFM 29: 45–71

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10``` ```x <- 1:10 * 1e6 Local_Pareto_Alpha(x, "norm", mean = 5e6, sd = 2e6) Local_Pareto_Alpha(x, "lnorm", meanlog = 0, sdlog = 4) Local_Pareto_Alpha(x, "gamma", shape = 5, rate = 1e-6) Local_Pareto_Alpha(x, "weibull", shape = 0.5, scale = 1e6) Local_Pareto_Alpha(x, "exp", rate = 1e-6) Local_Pareto_Alpha(x, "Pareto", t = 1e6, alpha = 1, truncation = 20e6) Local_Pareto_Alpha(x, "GenPareto", t = 1e6, alpha_ini = 1, alpha_tail = 2) Local_Pareto_Alpha(x, "PiecewisePareto", t = c(1e6, 3e6, 5e6), alpha = c(1, 2, 3), truncation = 20e6, truncation_type = "wd") ```

Pareto documentation built on March 3, 2021, 5:07 p.m.