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[heavy_tails] Update references and titles of figures #432

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May 8, 2024
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[heavy_tails] Update references and titles of figures #432

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[heavy_tails] Update references and titles of figures
SylviaZhaooo Apr 26, 2024
735bf78
Update heavy_tails.md
SylviaZhaooo May 7, 2024
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10 changes: 8 additions & 2 deletions lectures/heavy_tails.md
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Expand Up @@ -118,7 +118,7 @@ too much from the mean.
Putting this another way, light-tailed distributions are those that
rarely generate extreme values.

(A more formal definition is given [below](https://intro.quantecon.org/heavy_tails.html#light-and-heavy-tails).)
(A more formal definition is given {ref}`below <heavy-tail:formal-definition>`.)

Many statisticians and econometricians
use rules of thumb such as "outcomes more than four or five
Expand Down Expand Up @@ -262,7 +262,7 @@ like
* forecasting
* taxation (across a heavy-tailed income distribution), etc.

We return to these points [below](https://intro.quantecon.org/heavy_tails.html#why-do-heavy-tails-matter).
We return to these points {ref}`below <heavy-tail:application>`.



Expand Down Expand Up @@ -467,6 +467,8 @@ fig, ax = plt.subplots()
alpha = 1.0
ax.plot(x, np.exp(- alpha * x), label='exponential', alpha=0.8)
ax.plot(x, x**(- alpha), label='Pareto', alpha=0.8)
ax.set_xlabel('X value', fontsize=12)
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@SylviaZhaooo is the fontsize essential here?

ax.set_ylabel('CCDF', fontsize=12)
ax.legend()
plt.show()
```
Expand All @@ -479,6 +481,8 @@ fig, ax = plt.subplots()
alpha = 1.0
ax.loglog(x, np.exp(- alpha * x), label='exponential', alpha=0.8)
ax.loglog(x, x**(- alpha), label='Pareto', alpha=0.8)
ax.set_xlabel('log value', fontsize=12)
ax.set_ylabel('log prob', fontsize=12)
ax.legend()
plt.show()
```
Expand Down Expand Up @@ -848,6 +852,7 @@ The sequence shows no sign of converging.
We return to this point in the exercises.


(heavy-tail:application)=
## Why do heavy tails matter?

We have now seen that
Expand Down Expand Up @@ -925,6 +930,7 @@ nonnegative random variables and their distributions.
The definitions for
left hand tails are very similar and we omit them to simplify the exposition.

(heavy-tail:formal-definition)=
### Light and heavy tails

A distribution $F$ with density $f$ on $\mathbb R_+$ is called **heavy-tailed** if
Expand Down
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