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# upperparams

Upper Pareto tail parameters

## Syntax

``params = upperparams(pd)``

## Description

example

````params = upperparams(pd)` returns the two-element vector `params`, which includes the shape and scale parameters of the generalized Pareto distribution (GPD) in the upper tail of `pd`.`upperparams` does not return the location parameter of the GPD. The location parameter is the quantile value corresponding to the upper tail cumulative probability. Use the `boundary` function to return the location parameter.```

## Examples

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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 upper Pareto tail by using the object function `upperparams`.

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 upper tail by using the `upperparams` function.

`params = upperparams(pd)`
```params = 1×2 0.2487 3.0097 ```

You can also get the upper Pareto tail parameters by using the `UpperParameters` property. Access the `UpperParameters` property by using dot notation.

`pd.UpperParameters`
```ans = 1×2 0.2487 3.0097 ```

The location parameter of the GPD is equal to the quantile value of the upper 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(1)` is the location parameter of the GPD of the upper tail.

Use the `lowerparams` function or the `LowerParameters` property to get the lower Pareto tail parameters.

## Input Arguments

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

Introduced in R2007a

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