Lower Pareto tail parameters
returns the two-element vector
params = lowerparams(
params, which includes the shape
and scale parameters of the generalized Pareto distribution (GPD) in the lower tail
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.
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
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];
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
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.
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
[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.
upperparams function or the
UpperParameters property to get the upper Pareto tail parameters.