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.
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 =
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 = 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.
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.
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.