From 418a891812d5f6e59c8e1ac1179b23791a30ec79 Mon Sep 17 00:00:00 2001 From: JingkunZhao Date: Fri, 26 Apr 2024 17:55:55 +1000 Subject: [PATCH 1/2] [heavy_tails] Update references and titles of figures --- lectures/heavy_tails.md | 10 ++++++++-- 1 file changed, 8 insertions(+), 2 deletions(-) diff --git a/lectures/heavy_tails.md b/lectures/heavy_tails.md index b2b1756a..b4b117db 100644 --- a/lectures/heavy_tails.md +++ b/lectures/heavy_tails.md @@ -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 `.) Many statisticians and econometricians use rules of thumb such as "outcomes more than four or five @@ -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 `. @@ -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) +ax.set_ylabel('CCDF', fontsize=12) ax.legend() plt.show() ``` @@ -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() ``` @@ -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 @@ -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 From 735bf78ffebd771042449454263b21b899e32f50 Mon Sep 17 00:00:00 2001 From: JingkunZhao Date: Tue, 7 May 2024 11:04:36 +1000 Subject: [PATCH 2/2] Update heavy_tails.md --- lectures/heavy_tails.md | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/lectures/heavy_tails.md b/lectures/heavy_tails.md index b4b117db..b396ddb7 100644 --- a/lectures/heavy_tails.md +++ b/lectures/heavy_tails.md @@ -467,8 +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) -ax.set_ylabel('CCDF', fontsize=12) +ax.set_xlabel('X value') +ax.set_ylabel('CCDF') ax.legend() plt.show() ``` @@ -481,8 +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.set_xlabel('log value') +ax.set_ylabel('log prob') ax.legend() plt.show() ```