# Documentation

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# pdf

Class: piecewisedistribution

Probability density function for piecewise distribution

## Syntax

```P = pdf(obj,X) ```

## Description

`P = pdf(obj,X)` returns an array `P` of values of the probability density function for the piecewise distribution object `obj`, evaluated at the values in the array `X`.

### Note

For a Pareto tails object, the pdf is computed using the generalized Pareto distribution in the tails. In the center, the pdf is computed using the slopes of the cdf, which are interpolated between a set of discrete values. Therefore the pdf in the center is piecewise constant. It is noisy for a `cdffun` specified in `paretotails` via the `'ecdf'` option, and somewhat smoother for the `'kernel'` option, but generally not a good estimate of the underlying density of the original data.

## Examples

Fit Pareto tails to a t distribution at cumulative probabilities 0.1 and 0.9:

```t = trnd(3,100,1); obj = paretotails(t,0.1,0.9); [p,q] = boundary(obj) p = 0.1000 0.9000 q = -1.7766 1.8432 pdf(obj,q) ans = 0.2367 0.1960```