spec: add pp-basic specification (#4607)

## New Specification: `pp-basic`

Related to #4587

---

### specification.md

# pp-basic: Probability-Probability (P-P) Plot

## Description

A diagnostic plot comparing the cumulative distribution function (CDF)
of observed data against a theoretical distribution by plotting
empirical CDF values against theoretical CDF values. Unlike Q-Q plots
which compare quantiles, P-P plots compare cumulative probabilities on
both axes (0 to 1), making them more sensitive to deviations in the
center of the distribution. Points falling along the 45-degree diagonal
indicate a good fit.

## Applications

- Assessing whether sample data follows a hypothesized distribution
(e.g., normality testing for regression residuals)
- Reliability engineering: selecting the best-fit distribution for
failure time data
- Quality control: verifying process measurements conform to expected
distributional assumptions

## Data

- `observed` (numeric) - Sample data values drawn from an unknown
distribution
- `theoretical_distribution` (string) - Name of the theoretical
distribution to compare against (e.g., normal)
- Size: 50-500 data points
- Example: 200 samples from a slightly skewed distribution compared
against a normal reference

## Notes

- Both axes range from 0 to 1 (cumulative probabilities)
- Include a 45-degree reference line representing perfect distributional
fit
- Use a square aspect ratio to preserve the visual meaning of the
diagonal
- Sort observed data and compute empirical CDF as i/(n+1) or similar
plotting position formula
- Evaluate theoretical CDF using fitted or specified distribution
parameters
- S-shaped deviations from the diagonal suggest the data has heavier or
lighter tails than the reference distribution

---

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plots/pp-basic/specification.md

@@ -0,0 +1,27 @@
+# pp-basic: Probability-Probability (P-P) Plot
+
+## Description
+
+A diagnostic plot comparing the cumulative distribution function (CDF) of observed data against a theoretical distribution by plotting empirical CDF values against theoretical CDF values. Unlike Q-Q plots which compare quantiles, P-P plots compare cumulative probabilities on both axes (0 to 1), making them more sensitive to deviations in the center of the distribution. Points falling along the 45-degree diagonal indicate a good fit.
+
+## Applications
+
+- Assessing whether sample data follows a hypothesized distribution (e.g., normality testing for regression residuals)
+- Reliability engineering: selecting the best-fit distribution for failure time data
+- Quality control: verifying process measurements conform to expected distributional assumptions
+
+## Data
+
+- `observed` (numeric) - Sample data values drawn from an unknown distribution
+- `theoretical_distribution` (string) - Name of the theoretical distribution to compare against (e.g., normal)
+- Size: 50-500 data points
+- Example: 200 samples from a slightly skewed distribution compared against a normal reference
+
+## Notes
+
+- Both axes range from 0 to 1 (cumulative probabilities)
+- Include a 45-degree reference line representing perfect distributional fit
+- Use a square aspect ratio to preserve the visual meaning of the diagonal
+- Sort observed data and compute empirical CDF as i/(n+1) or similar plotting position formula
+- Evaluate theoretical CDF using fitted or specified distribution parameters
+- S-shaped deviations from the diagonal suggest the data has heavier or lighter tails than the reference distribution

plots/pp-basic/specification.yaml

@@ -0,0 +1,28 @@
+# Specification-level metadata for pp-basic
+# Auto-synced to PostgreSQL on push to main
+
+spec_id: pp-basic
+title: Probability-Probability (P-P) Plot
+
+# Specification tracking
+created: "2026-03-06T19:54:34Z"
+updated: null
+issue: 4587
+suggested: MarkusNeusinger
+
+# Classification tags (applies to all library implementations)
+# See docs/reference/tagging-system.md for detailed guidelines
+tags:
+  plot_type:
+    - pp
+    - calibration
+  data_type:
+    - numeric
+    - continuous
+  domain:
+    - statistics
+    - general
+  features:
+    - basic
+    - distribution
+    - 2d