@@ -118,7 +118,7 @@ too much from the mean.
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Putting this another way, light-tailed distributions are those that
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rarely generate extreme values.
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- (A more formal definition is given [ below] ( https://intro.quantecon.org/heavy_tails.html#light-and- heavy-tails ) .)
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+ (A more formal definition is given {ref} ` below < heavy-tail:formal-definition> ` .)
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Many statisticians and econometricians
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use rules of thumb such as "outcomes more than four or five
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* forecasting
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* taxation (across a heavy-tailed income distribution), etc.
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- We return to these points [ below] ( https://intro.quantecon.org/heavy_tails.html#why-do- heavy-tails-matter ) .
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+ We return to these points {ref} ` below < heavy-tail:application> ` .
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@@ -467,6 +467,8 @@ fig, ax = plt.subplots()
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alpha = 1.0
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ax.plot(x, np.exp(- alpha * x), label='exponential', alpha=0.8)
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ax.plot(x, x**(- alpha), label='Pareto', alpha=0.8)
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+ ax.set_xlabel('X value', fontsize=12)
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+ ax.set_ylabel('CCDF', fontsize=12)
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ax.legend()
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plt.show()
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```
@@ -479,6 +481,8 @@ fig, ax = plt.subplots()
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alpha = 1.0
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ax.loglog(x, np.exp(- alpha * x), label='exponential', alpha=0.8)
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ax.loglog(x, x**(- alpha), label='Pareto', alpha=0.8)
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+ ax.set_xlabel('log value', fontsize=12)
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+ ax.set_ylabel('log prob', fontsize=12)
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ax.legend()
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plt.show()
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```
@@ -848,6 +852,7 @@ The sequence shows no sign of converging.
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We return to this point in the exercises.
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+ (heavy-tail: application )=
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## Why do heavy tails matter?
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We have now seen that
@@ -925,6 +930,7 @@ nonnegative random variables and their distributions.
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The definitions for
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left hand tails are very similar and we omit them to simplify the exposition.
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+ (heavy-tail: formal-definition )=
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### Light and heavy tails
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A distribution $F$ with density $f$ on $\mathbb R_ +$ is called ** heavy-tailed** if
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