Local_Pareto_Alpha function

Local Pareto Alpha

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

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

Returns

Local Pareto alpha of the selected distribution at x

Examples

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")

References

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