lowerparams

Lower Pareto tail parameters

Syntax

params = lowerparams(pd)

Description

params = lowerparams(pd) returns the two-element vector params, which includes the shape and scale parameters of the generalized Pareto distribution (GPD) in the lower tail of pd.

lowerparams does not return the location parameter of the GPD. The location parameter is the quantile value corresponding to the lower tail cumulative probability. Use the boundary function to return the location parameter.

Examples

Parameters of Lower Pareto Tail

Generate a sample data set and fit a piecewise distribution with Pareto tails to the data by using paretotails. Find the distribution parameters of the lower Pareto tail by using the object function lowerparams.

Generate a sample data set containing 20% outliers.

rng('default');  % For reproducibility
left_tail = -exprnd(1,100,1);
right_tail = exprnd(5,100,1);
center = randn(800,1);
x = [left_tail;center;right_tail];

Create a paretotails object by fitting a piecewise distribution to x. Specify the boundaries of the tails using the lower and upper tail cumulative probabilities so that a fitted object consists of the empirical distribution for the middle 80% of the data set and GPDs for the lower and upper 10% of the data set.

pd = paretotails(x,0.1,0.9)

pd = 
Piecewise distribution with 3 segments
      -Inf < x < -1.33251    (0 < p < 0.1): lower tail, GPD(-0.0063504,0.567017)
   -1.33251 < x < 1.80149  (0.1 < p < 0.9): interpolated empirical cdf
        1.80149 < x < Inf    (0.9 < p < 1): upper tail, GPD(0.24874,3.00974)

Return the shape and scale parameters of the fitted GPD of the lower tail by using the lowerparams function.

params = lowerparams(pd)

params = 1×2

   -0.0064    0.5670

You can also get the lower Pareto tail parameters by using the LowerParameters property. Access the LowerParameters property by using dot notation.

pd.LowerParameters

ans = 1×2

   -0.0064    0.5670

The location parameter of the GPD is equal to the quantile value of the lower tail cumulative probability. Return the location parameter by using the boundary function.

[p,q] = boundary(pd)

p = 2×1

    0.1000
    0.9000

q = 2×1

   -1.3325
    1.8015

The values in p are the cumulative probabilities at the boundaries, and the values in q are the corresponding quantiles. q(2) is the location parameter of the GPD of the lower tail.

Use the upperparams function or the UpperParameters property to get the upper Pareto tail parameters.

Input Arguments

pd — Piecewise distribution with Pareto tails

paretotails object

Piecewise distribution with Pareto tails, specified as a paretotails object.