PNP_fit: Fitting a Pareto-Normal-Pareto Model

Description

GNG_fit is used to fit three components composite models with components Pareto, normal and Pareto.

Usage

PNP_fit(
  data,
  start = c(break1 = -0.02, break2 = 0.02, mean = 0, sd = 0.012),
  ...
)

Value

A list of class comp_fit.

Arguments

data: vector of values to which the density is optimized.
start: named vector (break1, break2, mean, sd) of values that are used to start the optimization, default: c(break1 = -0.02, break2 = 0.02, mean = 0, sd = 0.012).
...: further arguments to be passed to optimizer.

Details

The PNP model is the Pareto-Normal-Pareto model. This means that a \(-X\) transformation of a Pareto random variable will be used for the left tail, normal distribution for the center and again Pareto for the right tail.

The code uses the maximum likelihood estimation technique to estimate the four parameters from the start vector (break1, break2, mean, sd). The other parameters (shape parameters of Pareto distribution) are computed in each step such that the function is continuous. Weights are estimated in every step as a proportion of points that correspond to each of the truncated region.

Optimization is handled by the mle2 function.

Examples

Run this code

if (FALSE) {
 PNP_fit(stocks$SAP)

 PNP_fit(stocks$MSFT)

 autoplot(PNP_fit(stocks$ADS))

 PNP_fit(stocks$GSPC, method = "BFGS")

 PNP_fit(stocks$DJI, start = c(-0.01,0.01,0,0.008))

}