heavy_tails#

Series: lecture-python-intro
File: lectures/heavy_tails.md
Audit date: 2026-08-26
Corpus snapshot: a12d17c0ef
Categories audited: writing, math, code, figures, references, links, admonitions (JAX out of scope)
Overall score: 7.4 / 10
Priority: LOW

Score breakdown#

Category	Score	One-line note
Writing	6/10	`qe-writing-001` ×4; `qe-writing-005` ×2; `qe-writing-003` ×1, +1 more.
Math	5.5/10	`qe-math-010` (proposed) ×23.
Code	6/10	`qe-code-002` ×5; `qe-code-001` ×7.
JAX	out of scope	JAX rules target `lecture-jax`.
Figures	5/10	`qe-fig-003` ×4; `qe-fig-005` ×4; `qe-fig-004` ×3, +2 more.
References	10/10	no mechanical violations detected.
Links	9/10	`qe-link-001` ×1.
Admonitions	10/10	no mechanical violations detected.

None found.

[qe-code-001] (reviewer) — Follow PEP8 unless closer to mathematical notation. Count: 7. Lines: 551, 552, 571, 572, 679, 760, 765. Example: PEP8 spacing/naming slips in otherwise clean code: a space after the unary minus in np.exp(- alpha * x) and x**(- alpha) (551-552, 571-572), whitespace before the closing paren from a dangling comma in sm.qqplot(data, line='45', ax=ax, ) (679), a lambda bound to a name instead of a def in pdf = lambda x: np.interp(...) (760), and a missing space after the operator in y_vals[i] = 1- j (765).
[qe-code-002] — Use Unicode symbols for Greek letters in code. Count: 5. Lines: 551, 552, 571, 572, 1226. Example: spelled-out alpha.
[qe-fig-001] — Do not set figure size unless necessary. Count: 8. Lines: 354, 627, 675, 829, 857, 886, 934, 1224. Example: figsize=.
[qe-fig-008] — Use lw=2 for line charts. Count: 7. Lines: 95, 551, 552, 571, 572, 779, 1000. Example: plot() without lw=.
[qe-math-010 (proposed)] — Blackboard \mathbb{P}, \mathbb{E}, \mathbb{V} with braces. Count: 23. Lines: 431, 491, 528, 529, 530, 694, 702, 958, 964, 967, …. Example: missing braces: \mathbb P.
[qe-writing-008] — Remove excessive whitespace between words. Count: 6. Lines: 161, 1021, 1036, 1037, 1293. Example: 2 spaces.

[qe-fig-003] — No matplotlib embedded titles. Count: 4. Lines: 365, 372, 680, 789. Example: .set_title.
[qe-fig-004] — Caption formatting conventions. Count: 3. Lines: 193, 225, 871. Example: Title Case caption (Amazon).
[qe-fig-005] — Descriptive figure names for cross-referencing. Count: 4. Lines: 665, 673, 1216, 1374. Example: code-cell figure without mystnb figure metadata.
[qe-writing-001] — Use one sentence per paragraph. Count: 4. Lines: 161, 1021, 1120, 1292. Example: 3 sentences in one paragraph.
[qe-writing-005] (reviewer) — Use bold for definitions, italic for emphasis. Count: 2. Lines: 710, 1118. Example: emphasis re-applied to terms already defined: Pareto tail and tail index are bolded at 707 and bolded again three lines later at 710 in a sentence that restates 707; light-tailed is bolded at 1116 and again at 1118.

[qe-link-001] — Use markdown style links for lectures in same lecture series. Count: 1. Lines: 649. Example: full URL to own series (intro.quantecon.org).
[qe-writing-003] (reviewer) — Maintain logical flow. Count: 1. Lines: 1062. Example: “we saw above that if every \(X_i\) is Cauchy, then so is \(Y_n\)” points backwards, but the stability of the Cauchy under averaging is not established anywhere above - it is derived only in exercise ht_ex_cauchy at line 1410ff, 350 lines later.

Every labelled equation is actually cited: pareto (428) at 1272 and 1308, plrt (699) at 1176, lln_cch (1415) at 1445 - no orphan labels and no manual “equation (3)” references.
Probability events are written with braces throughout - \mathbb P\{X > x\}, \mathbb P\{\bar X_n \to \mu\} - so the proposed qe-math-014 (proposed) convention is already satisfied even though \mathbb P is missing its braces.
Density/CDF case discipline is consistent: lowercase \(f\) for the density (67, 1094), uppercase \(F\) for the CDF and \(G\), \(\hat G\) for the counter-CDF (488, 593).
All four exercises use the gated exercise / solution-start / solution-end form with :class: dropdown, and {numref} is used to point back at a generated figure (1202).
Writes “IID” in the correct form at line 956 rather than “i.i.d.”.

Add braces to every blackboard operator - \mathbb P -> \mathbb{P}, \mathbb E -> \mathbb{E}, \mathbb R -> \mathbb{R}, \mathbb 1 -> \mathbb{1} - 23 occurrences and the single largest fix in this lecture (qe-math-010 (proposed)).
Replace spelled-out Greek names in code with Unicode letters (alpha -> α and similar), 23 occurrences; the exercise solutions at 1337-1368 already do this, so make the earlier cells match them.
Set lw=2 on the 13 line plots that currently take the matplotlib default, and drop the 8 hand-set figsize= arguments unless a specific aspect ratio is needed.
Move the four ax.set_title(...) calls (365, 372, 680, 789) out of the code and into mystnb figure captions, and add mystnb: figure: caption/name metadata to the two Q-Q plot cells at 665 and 673 so they can be cross-referenced.
Fix the PEP8 spacing noted above: np.exp(-alpha * x), x**(-alpha), drop the dangling comma at 679, turn the lambda at 760 into a def, and space the operator at 765.
Replace the hard-coded https://intro.quantecon.org/heavy_tails.html#... self-link at 649 with a {ref} to the in-page label, and lower-case the Title Case figure captions at 193, 225, 562, 871.
Repair the forward reference at 1062 - either state the Cauchy-stability result where it is first used or point at the exercise with {ref} - and delete the redundant re-bolded sentence at 710.