Merge pull request #307 from jorenham/know-lmoments

Exact L-moments of several distributions

.editorconfig

@@ -9,7 +9,6 @@ indent_style = space
 indent_size = 4
 insert_final_newline = true
 trim_trailing_whitespace = true
-max_line_length = 79
 
 # 2 space indentation
 [{*.bib, *.json,*.jsonc,*.yaml,*.yml}]

.vscode/extensions.json

@@ -5,7 +5,8 @@
         "davidanson.vscode-markdownlint",
         "detachhead.basedpyright",
         "editorconfig.editorconfig",
-        "ms-python.python"
+        "ms-python.python",
+        "notzaki.pandocciter"
     ],
     "unwantedRecommendations": [
         "ms-pyright.pyright",

.vscode/settings.json

@@ -1 +1,19 @@
-{}
+{
+    "[python]": {
+        "editor.defaultFormatter": "charliermarsh.ruff",
+        "editor.rulers": [79, 130]
+    },
+    "[bibtex]": {
+        "editor.rulers": []
+    },
+    "[markdown]": {
+        "editor.rulers": [80]
+    },
+    "[markdown_latex_combined]": {
+        "editor.rulers": [80]
+    },
+    "markdown.extension.completion.root": "docs",
+    "PandocCiter.DefaultBib": "docs/refs.bib",
+    "PandocCiter.DefaultBibs": ["docs"],
+    "python.testing.pytestEnabled": true
+}

docs/api/distributions.md

@@ -1,20 +1,36 @@
 # Probability Distributions
 
-<!-- TODO: custom listing -->
-
-::: lmo.distributions
-    options:
-      heading_level: 2
-
 ## `scipy.stats` integration
 
 <!-- TODO: Describe this -->
 <!-- TODO: Short example -->
 
-::: lmo.contrib.scipy_stats
+::: lmo.contrib.scipy_stats.l_rv_generic
+    options:
+      show_bases: false
+      show_root_full_path: false
+      show_root_members_full_path: false
+
+## Parametric
+
+::: lmo.distributions.kumaraswamy
+    options:
+      show_symbol_type_heading: false
+      show_labels: false
+::: lmo.distributions.wakeby
+    options:
+      show_symbol_type_heading: false
+      show_labels: false
+::: lmo.distributions.genlambda
+    options:
+      show_symbol_type_heading: false
+      show_labels: false
+
+## Nonparametric
+
+::: lmo.distributions.l_poly
     options:
-      heading_level: 3
-      show_root_heading: false
-      show_root_toc_entry: false
-      members:
-      - l_rv_generic
+      group_by_category: false
+      show_labels: false
+      filters:
+        - "!^(a|b|random_state)$"

docs/distributions.md

@@ -1,5 +1,10 @@
+---
+hide:
+  - navigation
+---
+
 <!-- markdownlint-disable MD051 MD052 -->
-# L-moments of common probability distributions
+# Exact L-moments of probability distributions
 
 This page lists theoretical L-moments [@hosking1990] of popular probability
 distributions.
@@ -33,14 +38,14 @@ Numerical calculation of these L-statistics using [`scipy.stats`][scipy.stats]
 distributions, refer to
 [`rv_continuous.l_stats`][lmo.contrib.scipy_stats.l_rv_generic.l_stats].
 
-For direct calculation of the L-stats from a CDF or PPF, see
-[`l_stats_from_cdf`][lmo.theoretical.l_stats_from_cdf] or
-[`l_stats_from_ppf`][lmo.theoretical.l_stats_from_ppf], respectively.
+For direct calculation of the L-stats from a CDF or PPF function, see
+
+- [`lmo.theoretical.l_stats_from_cdf`][lmo.theoretical.l_stats_from_cdf]
+- [`lmo.theoretical.l_stats_from_ppf`][lmo.theoretical.l_stats_from_ppf]
 ///
 
-An overview of the L-location, L-scale, L-skewness and L-kurtosis,
-of a bunch of popular univariate probability distributions, for which they
-exist (in closed form).
+An overview of the exact L-location, L-scale, L-skewness and L-kurtosis
+of some well-known (univariate) probability distributions.
 
 ### L-stats
 
@@ -782,8 +787,8 @@ compactly expressed as
         & \text{if } \alpha = 0 \wedge r = 1 \\
     \displaystyle \frac{1}{\alpha r} \left[
         \frac
-            {\B(t + 1 - \alpha,\ r - 1 + \alpha)}
-            {\B(r + s + t - 1 - \alpha,\ \alpha)}
+            {\B(r + \alpha - 1,\ t - \alpha + 1)}
+            {\B(\alpha,\ r + s + t - \alpha + 1)}
         - \ffact{1}{r}
     \right]
         & \text{otherwise,}
@@ -824,7 +829,7 @@ There are several notable special cases of the GPD:
 
 ### Burr III / Dagum
 
-The *Burr III* distribution [^BURR], also known as the
+The *Burr III* distribution [@burr1942], also known as the
 [*Dagum distribution*](https://wikipedia.org/wiki/Dagum_distribution), has two
 shape parameters \( \alpha \) and \( \beta \), both restricted to the
 positive reals
@@ -964,7 +969,7 @@ Its general \( r \)-th trimmed L-moment are:
 \tlmoment{s,t}{r} =
     \frac{1}{r}
     \sum_{k = t + 1}^{r + s + t}
-        (-1)^{k - 1}
+        (-1)^{k - t - 1}
         \binom{r + k - 2}{r + t - 1}
         \binom{r + s + t}{k}
         \frac{\B\bigl(1 / \alpha,\ 1 + k \beta \bigr)}{\alpha}

docs/examples/lmm.ipynb

@@ -1,12 +1,5 @@
 {
  "cells": [
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Fitting the Generalized Extreme Value Distribution "
-   ]
-  },
   {
    "cell_type": "code",
    "execution_count": 1,

docs/examples/visual_intro.ipynb

@@ -4,14 +4,12 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# "
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# A visual introduction to L-moments\n"
+    "## Required dependencies\n",
+    "\n",
+    "This notebook requires that you have \n",
+    "[`matplotlib`](https://pypi.org/project/matplotlib/) installed,\n",
+    "and, of course, [Lmo](https://pypi.org/project/lmo/) (preferrably the latest\n",
+    "stable release)."
    ]
   },
   {

docs/styles/theme.css

@@ -45,11 +45,15 @@ tr.row-double-top > td {
     border-top: 0.15rem double var(--md-typeset-table-color) !important;
 }
 
+.md-grid {
+    max-width: 1440px;
+}
+
 /* Workarounds */
-td,
+/* td,
 th {
     white-space: nowrap;
-}
+} */
 .md-typeset__scrollwrap > .md-typeset__table > table,
 .md-typeset div.arithmatex {
     overflow-y: hidden;

lmo/_lm.py

@@ -329,7 +329,7 @@ def l_moment(
             - $(0, 0)$ or $(0)$: The original **L**-moment, introduced by
                 Hosking in 1990.
             - $(t, t)$ or $(t)$: **TL**-moment (**T**rimmed L-moment)
-                $\\lambda_r^t$, with symmetric trimming. First introduced by
+                $\lambda_r^{(t)}$, with symmetric trimming. First introduced by
                 Elamir & Seheult in 2003, and refined by Hosking in 2007.
                 Generally more robust than L-moments. Useful for fitting
                 pathological distributions, such as the Cauchy distribution.