Exercise

# KDE of a loss distribution

Kernel density estimation (KDE) can fit distributions with 'fat tails', i.e. distributions with occasionally large deviations from the mean (such as the distribution of portfolio losses).

In Chapter 2 you learned about the Student's **T** distribution, which for low degrees of freedom can *also* capture this feature of portfolio losses.

You'll compare a Gaussian KDE with a **T** distribution, each fitted to provided portfolio `losses`

from 2008 - 2009. You'll visualize the relative fits of each using a histogram. (Recall the **T** distribution uses fitted parameters `params`

, while the `gaussian_kde`

, being *non-parametric*, returns a function.)

The function `gaussian_kde()`

is available, as is the `t`

distribution, both from `scipy.stats`

. Plots may be added to the provided `axis`

object.

Instructions

**100 XP**

- Fit a
`t`

distribution to portfolio`losses`

. - Fit a Gaussian KDE to
`losses`

by using`gaussian_kde()`

. - Plot the probability density functions (PDFs) of both estimates against
`losses`

, using the`axis`

object.