From 7f689263aaca5983659dea08a8ad01a8b137e783 Mon Sep 17 00:00:00 2001
From: "github-actions[bot]"
 <41898282+github-actions[bot]@users.noreply.github.com>
Date: Sun, 5 Apr 2026 12:15:25 +0000
Subject: [PATCH 1/2] Fix ChiSquared.InvCDF scale parameter bug; add InvCDF
 tests
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ChiSquared.InvCDF delegates to Gamma.InvCDF, but was passing
beta = 1/2 (rate) while FSharp.Stats Gamma uses the *scale*
parameterisation (Mean = alpha * scale).

The correct scale for Chi-squared(dof) = Gamma(alpha=dof/2, scale=2)
is 2.0, not 0.5.  The wrong value caused InvCDF to return quantiles
that were roughly 4× too small.

Also adds a testList "ChiSquared.InvCDF tests" with:
- boundary checks (p=0 → 0, p=1 → +∞)
- round-trip tests (CDF(InvCDF(p)) ≈ p) at p=0.5, 0.95, 0.01
- known-value tests derived from the existing CDF reference values

All 1201 tests pass.

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
---
 .../Distributions/Continuous/ChiSquared.fs    |  5 +-
 .../DistributionsContinuous.fs                | 59 +++++++++++++++++++
 2 files changed, 63 insertions(+), 1 deletion(-)

diff --git a/src/FSharp.Stats/Distributions/Continuous/ChiSquared.fs b/src/FSharp.Stats/Distributions/Continuous/ChiSquared.fs
index 44aa14ac..5fdc11a8 100644
--- a/src/FSharp.Stats/Distributions/Continuous/ChiSquared.fs
+++ b/src/FSharp.Stats/Distributions/Continuous/ChiSquared.fs
@@ -140,8 +140,11 @@ type ChiSquared =
     /// <param name="p">The probability value in [0.0, 1.0].</param>
     /// <returns>The quantile corresponding to the cumulative probability p.</returns>
     static member InvCDF (dof: float) (p: float) : float =
+        // Chi-squared(dof) = Gamma(alpha=dof/2, scale=2).
+        // FSharp.Stats Gamma uses the scale parameterisation (Mean = alpha * scale),
+        // so the correct scale is 2.0, not 1/2.
         let alpha = dof / 2.0
-        let beta  = 1. / 2.0
+        let beta  = 2.0
         Gamma.InvCDF alpha beta p
 
     /// <summary>Returns the support of the exponential distribution: [0, Positive Infinity).</summary>
diff --git a/tests/FSharp.Stats.Tests/DistributionsContinuous.fs b/tests/FSharp.Stats.Tests/DistributionsContinuous.fs
index 6d13c751..c674cad2 100644
--- a/tests/FSharp.Stats.Tests/DistributionsContinuous.fs
+++ b/tests/FSharp.Stats.Tests/DistributionsContinuous.fs
@@ -618,6 +618,65 @@ let chiSquaredTests =
                 Expect.floatClose Accuracy.veryHigh (testCase.PDF -1.) 0. "Should be equal"
                 Expect.isTrue (Ops.isNan <| testCase.PDF nan) "Should be equal"
         ]
+
+        // Tests for ChiSquared.InvCDF (the percentile-point function).
+        // Reference values from standard chi-square tables (and CDF values already tested above).
+        testList "ChiSquared.InvCDF tests" [
+
+            test "ChiSquared.InvCDF returns 0.0 for p=0.0" {
+                let x = Continuous.ChiSquared.InvCDF 5. 0.
+                Expect.floatClose Accuracy.high x 0. "InvCDF(p=0) should be 0"
+            }
+
+            test "ChiSquared.InvCDF returns +∞ for p=1.0" {
+                let x = Continuous.ChiSquared.InvCDF 5. 1.
+                Expect.isTrue (x = infinity) "InvCDF(p=1) should be +infinity"
+            }
+
+            // Round-trip tests: CDF(InvCDF(p)) ≈ p
+            test "ChiSquared.InvCDF round-trip dof=5 p=0.5" {
+                let dof = 5.
+                let p   = 0.5
+                let x   = Continuous.ChiSquared.InvCDF dof p
+                let p2  = Continuous.ChiSquared.CDF dof x
+                Expect.floatClose Accuracy.high p p2 "CDF(InvCDF(0.5)) ≈ 0.5"
+            }
+
+            test "ChiSquared.InvCDF round-trip dof=1 p=0.95" {
+                let dof = 1.
+                let p   = 0.95
+                let x   = Continuous.ChiSquared.InvCDF dof p
+                let p2  = Continuous.ChiSquared.CDF dof x
+                Expect.floatClose Accuracy.high p p2 "CDF(InvCDF(0.95)) ≈ 0.95"
+            }
+
+            test "ChiSquared.InvCDF round-trip dof=10 p=0.01" {
+                let dof = 10.
+                let p   = 0.01
+                let x   = Continuous.ChiSquared.InvCDF dof p
+                let p2  = Continuous.ChiSquared.CDF dof x
+                Expect.floatClose Accuracy.high p p2 "CDF(InvCDF(0.01)) ≈ 0.01"
+            }
+
+            // Known-value tests derived from the CDF cases tested above
+            // (Williams 1984 table: CDF(20, 12.443) ≈ 0.1  →  InvCDF(20, 0.1) ≈ 12.443)
+            test "ChiSquared.InvCDF known value dof=20 p=0.1" {
+                let x = Continuous.ChiSquared.InvCDF 20. 0.1
+                Expect.floatClose Accuracy.low x 12.443 "InvCDF(20, 0.1) should be ≈ 12.443"
+            }
+
+            // CDF(3, 1.424) ≈ 0.3  →  InvCDF(3, 0.3) ≈ 1.424
+            test "ChiSquared.InvCDF known value dof=3 p=0.3" {
+                let x = Continuous.ChiSquared.InvCDF 3. 0.3
+                Expect.floatClose Accuracy.low x 1.424 "InvCDF(3, 0.3) should be ≈ 1.424"
+            }
+
+            // CDF(100, 129.561) ≈ 0.975  →  InvCDF(100, 0.975) ≈ 129.561
+            test "ChiSquared.InvCDF known value dof=100 p=0.975" {
+                let x = Continuous.ChiSquared.InvCDF 100. 0.975
+                Expect.floatClose Accuracy.low x 129.561 "InvCDF(100, 0.975) should be ≈ 129.561"
+            }
+        ]
     ]
 
 //Test ommitted due to long runtime of CodeCov

From 80f09b7699d29da44938ae24d25cba4b4c2a4c19 Mon Sep 17 00:00:00 2001
From: "github-actions[bot]" <github-actions[bot]@users.noreply.github.com>
Date: Sun, 5 Apr 2026 12:15:28 +0000
Subject: [PATCH 2/2] ci: trigger checks