From fe773689c503f46d5737c6c22086ad738a1b76a4 Mon Sep 17 00:00:00 2001
From: Brook <71849503+Primebrook@users.noreply.github.com>
Date: Thu, 6 Feb 2025 14:29:08 +0000
Subject: [PATCH 01/20] linting deps

---
 lib/exstatic/native.ex                |  1 -
 mix.exs                               | 18 ++++++++++++++++--
 mix.lock                              |  5 +++++
 test/exstatic/distribution/t_test.exs |  1 -
 4 files changed, 21 insertions(+), 4 deletions(-)

diff --git a/lib/exstatic/native.ex b/lib/exstatic/native.ex
index 691f3b5..9bcd5a3 100644
--- a/lib/exstatic/native.ex
+++ b/lib/exstatic/native.ex
@@ -35,4 +35,3 @@ defmodule Exstatic.Native do
   @spec standardized_t_variance(float()) :: {:ok, float()} | {:error, String.t()}
   def standardized_t_variance(_df), do: :erlang.nif_error(:nif_not_loaded)
 end
-
diff --git a/mix.exs b/mix.exs
index 54d02b5..c97eb03 100644
--- a/mix.exs
+++ b/mix.exs
@@ -5,8 +5,9 @@ defmodule Exstatic.MixProject do
     [
       app: :exstatic,
       version: "0.1.0",
-      elixir: "~> 1.17",
+      elixir: "~> 1.18",
       start_permanent: Mix.env() == :prod,
+      aliases: aliases(),
       deps: deps()
     ]
   end
@@ -18,10 +19,23 @@ defmodule Exstatic.MixProject do
     ]
   end
 
+  defp aliases do
+    [
+      lint: [
+        "compile --warnings-as-errors, dialyzer --plt",
+        "format",
+        "credo --all --mute-exit-status",
+        "dialyzer"
+      ]
+    ]
+  end
+
   # Run "mix help deps" to learn about dependencies.
   defp deps do
     [
-      {:rustler, "~> 0.35.1", runtime: false}
+      {:rustler, "~> 0.35.1", runtime: false},
+      {:credo, "~> 1.7", only: [:dev, :test], runtime: false},
+      {:dialyxir, "~> 1.4", only: [:dev, :test], runtime: false}
     ]
   end
 end
diff --git a/mix.lock b/mix.lock
index f83fd89..032c7ef 100644
--- a/mix.lock
+++ b/mix.lock
@@ -1,4 +1,9 @@
 %{
+  "bunt": {:hex, :bunt, "1.0.0", "081c2c665f086849e6d57900292b3a161727ab40431219529f13c4ddcf3e7a44", [:mix], [], "hexpm", "dc5f86aa08a5f6fa6b8096f0735c4e76d54ae5c9fa2c143e5a1fc7c1cd9bb6b5"},
+  "credo": {:hex, :credo, "1.7.11", "d3e805f7ddf6c9c854fd36f089649d7cf6ba74c42bc3795d587814e3c9847102", [:mix], [{:bunt, "~> 0.2.1 or ~> 1.0", [hex: :bunt, repo: "hexpm", optional: false]}, {:file_system, "~> 0.2 or ~> 1.0", [hex: :file_system, repo: "hexpm", optional: false]}, {:jason, "~> 1.0", [hex: :jason, repo: "hexpm", optional: false]}], "hexpm", "56826b4306843253a66e47ae45e98e7d284ee1f95d53d1612bb483f88a8cf219"},
+  "dialyxir": {:hex, :dialyxir, "1.4.5", "ca1571ac18e0f88d4ab245f0b60fa31ff1b12cbae2b11bd25d207f865e8ae78a", [:mix], [{:erlex, ">= 0.2.7", [hex: :erlex, repo: "hexpm", optional: false]}], "hexpm", "b0fb08bb8107c750db5c0b324fa2df5ceaa0f9307690ee3c1f6ba5b9eb5d35c3"},
+  "erlex": {:hex, :erlex, "0.2.7", "810e8725f96ab74d17aac676e748627a07bc87eb950d2b83acd29dc047a30595", [:mix], [], "hexpm", "3ed95f79d1a844c3f6bf0cea61e0d5612a42ce56da9c03f01df538685365efb0"},
+  "file_system": {:hex, :file_system, "1.1.0", "08d232062284546c6c34426997dd7ef6ec9f8bbd090eb91780283c9016840e8f", [:mix], [], "hexpm", "bfcf81244f416871f2a2e15c1b515287faa5db9c6bcf290222206d120b3d43f6"},
   "finch": {:hex, :finch, "0.19.0", "c644641491ea854fc5c1bbaef36bfc764e3f08e7185e1f084e35e0672241b76d", [:mix], [{:mime, "~> 1.0 or ~> 2.0", [hex: :mime, repo: "hexpm", optional: false]}, {:mint, "~> 1.6.2 or ~> 1.7", [hex: :mint, repo: "hexpm", optional: false]}, {:nimble_options, "~> 0.4 or ~> 1.0", [hex: :nimble_options, repo: "hexpm", optional: false]}, {:nimble_pool, "~> 1.1", [hex: :nimble_pool, repo: "hexpm", optional: false]}, {:telemetry, "~> 0.4 or ~> 1.0", [hex: :telemetry, repo: "hexpm", optional: false]}], "hexpm", "fc5324ce209125d1e2fa0fcd2634601c52a787aff1cd33ee833664a5af4ea2b6"},
   "hpax": {:hex, :hpax, "1.0.2", "762df951b0c399ff67cc57c3995ec3cf46d696e41f0bba17da0518d94acd4aac", [:mix], [], "hexpm", "2f09b4c1074e0abd846747329eaa26d535be0eb3d189fa69d812bfb8bfefd32f"},
   "jason": {:hex, :jason, "1.4.4", "b9226785a9aa77b6857ca22832cffa5d5011a667207eb2a0ad56adb5db443b8a", [:mix], [{:decimal, "~> 1.0 or ~> 2.0", [hex: :decimal, repo: "hexpm", optional: true]}], "hexpm", "c5eb0cab91f094599f94d55bc63409236a8ec69a21a67814529e8d5f6cc90b3b"},
diff --git a/test/exstatic/distribution/t_test.exs b/test/exstatic/distribution/t_test.exs
index f6d0ade..c3d24cf 100644
--- a/test/exstatic/distribution/t_test.exs
+++ b/test/exstatic/distribution/t_test.exs
@@ -68,4 +68,3 @@ defmodule Exstatic.Distribution.StandardizedTTest do
     end
   end
 end
-

From a8dbea8fc9d5c83e642a04e781d8550ca2d1dd60 Mon Sep 17 00:00:00 2001
From: Brook <71849503+Primebrook@users.noreply.github.com>
Date: Thu, 6 Feb 2025 14:35:01 +0000
Subject: [PATCH 02/20] test workflow

---
 .github/workflows/test.yml | 99 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 99 insertions(+)
 create mode 100644 .github/workflows/test.yml

diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
new file mode 100644
index 0000000..6e9685c
--- /dev/null
+++ b/.github/workflows/test.yml
@@ -0,0 +1,99 @@
+name: Test
+on:
+  push:
+    branches: [main]
+  pull_request:
+    branches: [main]
+jobs:
+  test:
+    name: Test (Elixir ${{ matrix.elixir }} | OTP ${{ matrix.otp }})
+    runs-on: ${{ matrix.os }}
+    strategy:
+      fail-fast: false
+      matrix:
+        include:
+          - elixir: 1.16.x
+            otp: 26
+            os: ubuntu-22.04
+          - elixir: 1.17.x
+            otp: 27
+            os: ubuntu-22.04
+          - elixir: 1.18.x
+            otp: 27
+            os: ubuntu-22.04
+    env:
+      MIX_ENV: test
+    steps:
+      - name: Setup Elixir
+        uses: erlef/setup-beam@v1
+        with:
+          elixir-version: ${{ matrix.elixir }}
+          otp-version: ${{ matrix.otp }}
+
+      - name: Checkout code
+        uses: actions/checkout@v4
+
+      - name: Cache dependencies
+        uses: actions/cache@v4
+        id: cache-deps
+        with:
+          path: |
+            deps
+            _build
+          key: |
+            mix-${{ runner.os }}-${{ matrix.elixir }}-${{ matrix.otp }}-${{ hashFiles('**/mix.lock') }}
+          restore-keys: |
+            mix-${{ runner.os }}-${{ matrix.elixir }}-${{ matrix.otp }}-
+      - name: Install dependencies
+        env:
+          HEX_API_KEY: ${{ secrets.HEX_API_KEY }}
+        run: mix deps.get
+
+      - name: Compile
+        run: mix compile --warnings-as-errors
+
+      - name: Check for unused packages
+        run: mix deps.unlock --check-unused
+
+      - run: mix format --check-formatted
+
+      - run: mix credo --strict
+
+      - run: mix dialyzer
+
+      - name: Check for abandonded packages
+        run: mix hex.audit
+
+      - name: Check outdated dependencies
+        run: mix hex.outdated --within-requirements || true
+
+      - name: Check for vulnerable packages
+        run: mix hex.audit
+
+      - name: Run tests
+        run: mix test
+
+      - name: Run tests (with coverage)
+        run: mix test --cover --export-coverage default
+
+      - name: Check coverage
+        run: mix test.coverage
+
+      - name: Scan for security vulnerabilities
+        run: mix sobelow --exit --threshold medium
+
+  publish:
+    name: Publish
+    runs-on: ubuntu-22.04
+    steps:
+      - uses: actions/checkout@v4
+      - uses: erlef/setup-beam@v1
+        with:
+          elixir-version: 1.18
+          otp-version: 27.2
+      - name: Fetch dependencies
+        run: mix deps.get
+      - name: Publish package
+        env:
+          HEX_API_KEY: ${{ secrets.HEX_API_KEY }}
+        run: mix hex.publish --organization ${{ vars.HEX_ORG }} --dry-run --replace --yes

From f595664052b3e01382a4b52f18e14e8879cb2a02 Mon Sep 17 00:00:00 2001
From: Brook <71849503+Primebrook@users.noreply.github.com>
Date: Thu, 6 Feb 2025 14:35:48 +0000
Subject: [PATCH 03/20] release workflow

---
 .github/workflows/release.yml | 20 ++++++++++++++++++++
 1 file changed, 20 insertions(+)
 create mode 100644 .github/workflows/release.yml

diff --git a/.github/workflows/release.yml b/.github/workflows/release.yml
new file mode 100644
index 0000000..69e0a1e
--- /dev/null
+++ b/.github/workflows/release.yml
@@ -0,0 +1,20 @@
+name: Release
+on:
+  release:
+    types: [published]
+jobs:
+  publish:
+    name: Publish
+    runs-on: ubuntu-22.04
+    steps:
+      - uses: actions/checkout@v4
+      - uses: erlef/setup-beam@v1
+        with:
+          elixir-version: 1.18
+          otp-version: 27.2
+      - name: Fetch dependencies
+        run: mix deps.get
+      - name: Publish package
+        env:
+          HEX_API_KEY: ${{ secrets.HEX_API_KEY }}
+        run: mix hex.publish --organization ${{ vars.HEX_ORG }} --replace --yes

From 6ed0be1f7cbb20f3287f4d836547576a353651d1 Mon Sep 17 00:00:00 2001
From: Brook <71849503+Primebrook@users.noreply.github.com>
Date: Thu, 6 Feb 2025 14:37:02 +0000
Subject: [PATCH 04/20] only test on 1.18

---
 .github/workflows/test.yml | 6 ------
 1 file changed, 6 deletions(-)

diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
index 6e9685c..cbe4714 100644
--- a/.github/workflows/test.yml
+++ b/.github/workflows/test.yml
@@ -12,12 +12,6 @@ jobs:
       fail-fast: false
       matrix:
         include:
-          - elixir: 1.16.x
-            otp: 26
-            os: ubuntu-22.04
-          - elixir: 1.17.x
-            otp: 27
-            os: ubuntu-22.04
           - elixir: 1.18.x
             otp: 27
             os: ubuntu-22.04

From d8175ccab8cc39a04e0fe801c99e77acc054581e Mon Sep 17 00:00:00 2001
From: Brook <71849503+Primebrook@users.noreply.github.com>
Date: Thu, 6 Feb 2025 14:56:53 +0000
Subject: [PATCH 05/20] package info

---
 README.md |  2 +-
 mix.exs   | 26 ++++++++++++++++++++++++--
 2 files changed, 25 insertions(+), 3 deletions(-)

diff --git a/README.md b/README.md
index dad766d..2ac021c 100644
--- a/README.md
+++ b/README.md
@@ -34,7 +34,7 @@ Normal.variance(dist)  # => 1.0
 
 ### Requirements
 
-- Elixir ~> 1.17
+- Elixir ~> 1.18
 
 Precompiled NIF binaries are included for common platforms. No additional system dependencies are required for normal usage.
 
diff --git a/mix.exs b/mix.exs
index c97eb03..43ab0e7 100644
--- a/mix.exs
+++ b/mix.exs
@@ -1,14 +1,22 @@
 defmodule Exstatic.MixProject do
   use Mix.Project
 
+  @version "0.1.0"
+  @source_url "https://github.com/intellection/exstatic"
+
   def project do
     [
       app: :exstatic,
-      version: "0.1.0",
+      version: @version,
       elixir: "~> 1.18",
       start_permanent: Mix.env() == :prod,
       aliases: aliases(),
-      deps: deps()
+      deps: deps(),
+      dialyzer: [plt_add_apps: [:mix]],
+      description: description(),
+      package: package(),
+      name: "Exstatic",
+      source_url: @source_url
     ]
   end
 
@@ -30,6 +38,20 @@ defmodule Exstatic.MixProject do
     ]
   end
 
+  defp description do
+    "A statistical distribution library for Elixir with native Rust implementations."
+  end
+
+  defp package do
+    [
+      name: "exstatic",
+      organization: "zappi",
+      files: ~w(lib .formatter.exs mix.exs README*),
+      licenses: ["MIT"],
+      links: %{"GitHub" => @source_url}
+    ]
+  end
+
   # Run "mix help deps" to learn about dependencies.
   defp deps do
     [

From a77e4d4c661b729176c4f15a751675f58873225c Mon Sep 17 00:00:00 2001
From: Brook <71849503+Primebrook@users.noreply.github.com>
Date: Thu, 6 Feb 2025 15:04:43 +0000
Subject: [PATCH 06/20] docs

---
 mix.exs | 12 +++++++++++-
 1 file changed, 11 insertions(+), 1 deletion(-)

diff --git a/mix.exs b/mix.exs
index 43ab0e7..fc778f1 100644
--- a/mix.exs
+++ b/mix.exs
@@ -14,6 +14,7 @@ defmodule Exstatic.MixProject do
       deps: deps(),
       dialyzer: [plt_add_apps: [:mix]],
       description: description(),
+      docs: docs(),
       package: package(),
       name: "Exstatic",
       source_url: @source_url
@@ -42,6 +43,14 @@ defmodule Exstatic.MixProject do
     "A statistical distribution library for Elixir with native Rust implementations."
   end
 
+  defp docs do
+    [
+      main: "readme",
+      source_ref: "v#{@version}",
+      extras: ["README.md", "CHANGELOG.md"]
+    ]
+  end
+
   defp package do
     [
       name: "exstatic",
@@ -57,7 +66,8 @@ defmodule Exstatic.MixProject do
     [
       {:rustler, "~> 0.35.1", runtime: false},
       {:credo, "~> 1.7", only: [:dev, :test], runtime: false},
-      {:dialyxir, "~> 1.4", only: [:dev, :test], runtime: false}
+      {:dialyxir, "~> 1.4", only: [:dev, :test], runtime: false},
+      {:ex_doc, "~> 0.34", only: :dev, runtime: false}
     ]
   end
 end

From f02db108cb06b29f4f0d5318dca3c5771f95c26c Mon Sep 17 00:00:00 2001
From: Brook <71849503+Primebrook@users.noreply.github.com>
Date: Thu, 6 Feb 2025 15:05:49 +0000
Subject: [PATCH 07/20] ex doc

---
 mix.lock | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/mix.lock b/mix.lock
index 032c7ef..74689b0 100644
--- a/mix.lock
+++ b/mix.lock
@@ -2,14 +2,20 @@
   "bunt": {:hex, :bunt, "1.0.0", "081c2c665f086849e6d57900292b3a161727ab40431219529f13c4ddcf3e7a44", [:mix], [], "hexpm", "dc5f86aa08a5f6fa6b8096f0735c4e76d54ae5c9fa2c143e5a1fc7c1cd9bb6b5"},
   "credo": {:hex, :credo, "1.7.11", "d3e805f7ddf6c9c854fd36f089649d7cf6ba74c42bc3795d587814e3c9847102", [:mix], [{:bunt, "~> 0.2.1 or ~> 1.0", [hex: :bunt, repo: "hexpm", optional: false]}, {:file_system, "~> 0.2 or ~> 1.0", [hex: :file_system, repo: "hexpm", optional: false]}, {:jason, "~> 1.0", [hex: :jason, repo: "hexpm", optional: false]}], "hexpm", "56826b4306843253a66e47ae45e98e7d284ee1f95d53d1612bb483f88a8cf219"},
   "dialyxir": {:hex, :dialyxir, "1.4.5", "ca1571ac18e0f88d4ab245f0b60fa31ff1b12cbae2b11bd25d207f865e8ae78a", [:mix], [{:erlex, ">= 0.2.7", [hex: :erlex, repo: "hexpm", optional: false]}], "hexpm", "b0fb08bb8107c750db5c0b324fa2df5ceaa0f9307690ee3c1f6ba5b9eb5d35c3"},
+  "earmark_parser": {:hex, :earmark_parser, "1.4.43", "34b2f401fe473080e39ff2b90feb8ddfeef7639f8ee0bbf71bb41911831d77c5", [:mix], [], "hexpm", "970a3cd19503f5e8e527a190662be2cee5d98eed1ff72ed9b3d1a3d466692de8"},
   "erlex": {:hex, :erlex, "0.2.7", "810e8725f96ab74d17aac676e748627a07bc87eb950d2b83acd29dc047a30595", [:mix], [], "hexpm", "3ed95f79d1a844c3f6bf0cea61e0d5612a42ce56da9c03f01df538685365efb0"},
+  "ex_doc": {:hex, :ex_doc, "0.37.0", "970f92b39e62c460aa8a367508e938f5e4da6e2ff3eaed3f8530b25870f45471", [:mix], [{:earmark_parser, "~> 1.4.42", [hex: :earmark_parser, repo: "hexpm", optional: false]}, {:makeup_c, ">= 0.1.0", [hex: :makeup_c, repo: "hexpm", optional: true]}, {:makeup_elixir, "~> 0.14 or ~> 1.0", [hex: :makeup_elixir, repo: "hexpm", optional: false]}, {:makeup_erlang, "~> 0.1 or ~> 1.0", [hex: :makeup_erlang, repo: "hexpm", optional: false]}, {:makeup_html, ">= 0.1.0", [hex: :makeup_html, repo: "hexpm", optional: true]}], "hexpm", "b0ee7f17373948e0cf471e59c3a0ee42f3bd1171c67d91eb3626456ef9c6202c"},
   "file_system": {:hex, :file_system, "1.1.0", "08d232062284546c6c34426997dd7ef6ec9f8bbd090eb91780283c9016840e8f", [:mix], [], "hexpm", "bfcf81244f416871f2a2e15c1b515287faa5db9c6bcf290222206d120b3d43f6"},
   "finch": {:hex, :finch, "0.19.0", "c644641491ea854fc5c1bbaef36bfc764e3f08e7185e1f084e35e0672241b76d", [:mix], [{:mime, "~> 1.0 or ~> 2.0", [hex: :mime, repo: "hexpm", optional: false]}, {:mint, "~> 1.6.2 or ~> 1.7", [hex: :mint, repo: "hexpm", optional: false]}, {:nimble_options, "~> 0.4 or ~> 1.0", [hex: :nimble_options, repo: "hexpm", optional: false]}, {:nimble_pool, "~> 1.1", [hex: :nimble_pool, repo: "hexpm", optional: false]}, {:telemetry, "~> 0.4 or ~> 1.0", [hex: :telemetry, repo: "hexpm", optional: false]}], "hexpm", "fc5324ce209125d1e2fa0fcd2634601c52a787aff1cd33ee833664a5af4ea2b6"},
   "hpax": {:hex, :hpax, "1.0.2", "762df951b0c399ff67cc57c3995ec3cf46d696e41f0bba17da0518d94acd4aac", [:mix], [], "hexpm", "2f09b4c1074e0abd846747329eaa26d535be0eb3d189fa69d812bfb8bfefd32f"},
   "jason": {:hex, :jason, "1.4.4", "b9226785a9aa77b6857ca22832cffa5d5011a667207eb2a0ad56adb5db443b8a", [:mix], [{:decimal, "~> 1.0 or ~> 2.0", [hex: :decimal, repo: "hexpm", optional: true]}], "hexpm", "c5eb0cab91f094599f94d55bc63409236a8ec69a21a67814529e8d5f6cc90b3b"},
+  "makeup": {:hex, :makeup, "1.2.1", "e90ac1c65589ef354378def3ba19d401e739ee7ee06fb47f94c687016e3713d1", [:mix], [{:nimble_parsec, "~> 1.4", [hex: :nimble_parsec, repo: "hexpm", optional: false]}], "hexpm", "d36484867b0bae0fea568d10131197a4c2e47056a6fbe84922bf6ba71c8d17ce"},
+  "makeup_elixir": {:hex, :makeup_elixir, "1.0.1", "e928a4f984e795e41e3abd27bfc09f51db16ab8ba1aebdba2b3a575437efafc2", [:mix], [{:makeup, "~> 1.0", [hex: :makeup, repo: "hexpm", optional: false]}, {:nimble_parsec, "~> 1.2.3 or ~> 1.3", [hex: :nimble_parsec, repo: "hexpm", optional: false]}], "hexpm", "7284900d412a3e5cfd97fdaed4f5ed389b8f2b4cb49efc0eb3bd10e2febf9507"},
+  "makeup_erlang": {:hex, :makeup_erlang, "1.0.2", "03e1804074b3aa64d5fad7aa64601ed0fb395337b982d9bcf04029d68d51b6a7", [:mix], [{:makeup, "~> 1.0", [hex: :makeup, repo: "hexpm", optional: false]}], "hexpm", "af33ff7ef368d5893e4a267933e7744e46ce3cf1f61e2dccf53a111ed3aa3727"},
   "mime": {:hex, :mime, "2.0.6", "8f18486773d9b15f95f4f4f1e39b710045fa1de891fada4516559967276e4dc2", [:mix], [], "hexpm", "c9945363a6b26d747389aac3643f8e0e09d30499a138ad64fe8fd1d13d9b153e"},
   "mint": {:hex, :mint, "1.6.2", "af6d97a4051eee4f05b5500671d47c3a67dac7386045d87a904126fd4bbcea2e", [:mix], [{:castore, "~> 0.1.0 or ~> 1.0", [hex: :castore, repo: "hexpm", optional: true]}, {:hpax, "~> 0.1.1 or ~> 0.2.0 or ~> 1.0", [hex: :hpax, repo: "hexpm", optional: false]}], "hexpm", "5ee441dffc1892f1ae59127f74afe8fd82fda6587794278d924e4d90ea3d63f9"},
   "nimble_options": {:hex, :nimble_options, "1.1.1", "e3a492d54d85fc3fd7c5baf411d9d2852922f66e69476317787a7b2bb000a61b", [:mix], [], "hexpm", "821b2470ca9442c4b6984882fe9bb0389371b8ddec4d45a9504f00a66f650b44"},
+  "nimble_parsec": {:hex, :nimble_parsec, "1.4.2", "8efba0122db06df95bfaa78f791344a89352ba04baedd3849593bfce4d0dc1c6", [:mix], [], "hexpm", "4b21398942dda052b403bbe1da991ccd03a053668d147d53fb8c4e0efe09c973"},
   "nimble_pool": {:hex, :nimble_pool, "1.1.0", "bf9c29fbdcba3564a8b800d1eeb5a3c58f36e1e11d7b7fb2e084a643f645f06b", [:mix], [], "hexpm", "af2e4e6b34197db81f7aad230c1118eac993acc0dae6bc83bac0126d4ae0813a"},
   "req": {:hex, :req, "0.5.8", "50d8d65279d6e343a5e46980ac2a70e97136182950833a1968b371e753f6a662", [:mix], [{:brotli, "~> 0.3.1", [hex: :brotli, repo: "hexpm", optional: true]}, {:ezstd, "~> 1.0", [hex: :ezstd, repo: "hexpm", optional: true]}, {:finch, "~> 0.17", [hex: :finch, repo: "hexpm", optional: false]}, {:jason, "~> 1.0", [hex: :jason, repo: "hexpm", optional: false]}, {:mime, "~> 2.0.6 or ~> 2.1", [hex: :mime, repo: "hexpm", optional: false]}, {:nimble_csv, "~> 1.0", [hex: :nimble_csv, repo: "hexpm", optional: true]}, {:plug, "~> 1.0", [hex: :plug, repo: "hexpm", optional: true]}], "hexpm", "d7fc5898a566477e174f26887821a3c5082b243885520ee4b45555f5d53f40ef"},
   "rustler": {:hex, :rustler, "0.35.1", "ec81961ef9ee833d721dafb4449cab29b16b969a3063a842bb9e3ea912f6b938", [:mix], [{:jason, "~> 1.0", [hex: :jason, repo: "hexpm", optional: false]}, {:req, "~> 0.5", [hex: :req, repo: "hexpm", optional: false]}, {:toml, "~> 0.6", [hex: :toml, repo: "hexpm", optional: false]}], "hexpm", "3713b2e70e68ec2bfa8291dfd9cb811fe64a770f254cd9c331f8b34fa7989115"},

From 5fb0cb0b59f43e94ee5909695574a8347944bf8c Mon Sep 17 00:00:00 2001
From: Brook <71849503+Primebrook@users.noreply.github.com>
Date: Thu, 6 Feb 2025 15:09:02 +0000
Subject: [PATCH 08/20] changelog

---
 CHANGELOG.md | 5 +++++
 1 file changed, 5 insertions(+)
 create mode 100644 CHANGELOG.md

diff --git a/CHANGELOG.md b/CHANGELOG.md
new file mode 100644
index 0000000..af61942
--- /dev/null
+++ b/CHANGELOG.md
@@ -0,0 +1,5 @@
+# Changelog
+
+## v0.1.0
+
+- Initial release.

From 788a5ca0e723fed31a59b73e45133cee3db0d1b8 Mon Sep 17 00:00:00 2001
From: Brook <71849503+Primebrook@users.noreply.github.com>
Date: Thu, 6 Feb 2025 15:20:11 +0000
Subject: [PATCH 09/20] moduledocs

---
 README.md                      |  2 +-
 lib/exstatic/continuous.ex     | 14 ++++++++++++++
 lib/exstatic/continuous_cdf.ex | 13 +++++++++++++
 lib/exstatic/distribution.ex   |  3 +++
 4 files changed, 31 insertions(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 2ac021c..66ef0d5 100644
--- a/README.md
+++ b/README.md
@@ -56,7 +56,7 @@ Full documentation can be found at [https://hexdocs.pm/exstatic](https://hexdocs
 
 ### Requirements
 
-- Elixir ~> 1.17
+- Elixir ~> 1.18
 - Rust (for compiling NIFs)
 
 ### Setup
diff --git a/lib/exstatic/continuous.ex b/lib/exstatic/continuous.ex
index 8506519..4e8f2aa 100644
--- a/lib/exstatic/continuous.ex
+++ b/lib/exstatic/continuous.ex
@@ -1,4 +1,18 @@
 defmodule Exstatic.Continuous do
+  @moduledoc """
+  Defines the behaviour for continuous probability distributions that support 
+  probability density function (PDF) calculations.
+
+  A continuous probability distribution is characterised by its probability 
+  density function (PDF), which describes the likelihood of different values 
+  occurring. 
+
+  This behaviour is implemented by distributions that can compute:
+
+  - `pdf/2` – the probability density at a given `x`
+  - `ln_pdf/2` – the natural logarithm of the probability density, often used 
+  for numerical stability.
+  """
   @type t() :: struct()
 
   @callback pdf(distribution :: t(), x :: float()) :: float()
diff --git a/lib/exstatic/continuous_cdf.ex b/lib/exstatic/continuous_cdf.ex
index 8b67750..b0148af 100644
--- a/lib/exstatic/continuous_cdf.ex
+++ b/lib/exstatic/continuous_cdf.ex
@@ -1,4 +1,17 @@
 defmodule Exstatic.ContinuousCDF do
+  @moduledoc """
+  Defines the behaviour for continuous probability distributions that support 
+  cumulative distribution function (CDF) and related calculations.
+
+  A cumulative distribution function (CDF) describes the probability that 
+  a random variable is less than or equal to a given value. This behaviour also 
+  supports related functions:
+
+  - `cdf/2` – computes P(X ≤ x), the cumulative probability.
+  - `sf/2` – computes P(X > x), also known as the survival function (SF).
+  - `inverse_cdf/2` – computes the quantile function, which finds `x` such 
+  that P(X ≤ x) = p.
+  """
   @type t() :: struct()
 
   @callback cdf(distribution :: t(), x :: float()) :: float()
diff --git a/lib/exstatic/distribution.ex b/lib/exstatic/distribution.ex
index 462f0da..6c768a4 100644
--- a/lib/exstatic/distribution.ex
+++ b/lib/exstatic/distribution.ex
@@ -1,4 +1,7 @@
 defmodule Exstatic.Distribution do
+  @moduledoc """
+  A behaviour for probability distributions.
+  """
   @type t() :: struct()
   @type error() :: {:error, atom()}
 

From 4215b00168a4eec64be616edf0f7d8d8dfa79939 Mon Sep 17 00:00:00 2001
From: Brook <71849503+Primebrook@users.noreply.github.com>
Date: Thu, 6 Feb 2025 15:22:56 +0000
Subject: [PATCH 10/20] rename behaviour Continuous -> ContinuousPDF

---
 lib/exstatic/{continuous.ex => continuous_pdf.ex} | 2 +-
 lib/exstatic/distribution/normal.ex               | 6 +++---
 lib/exstatic/distribution/t.ex                    | 4 ++--
 3 files changed, 6 insertions(+), 6 deletions(-)
 rename lib/exstatic/{continuous.ex => continuous_pdf.ex} (95%)

diff --git a/lib/exstatic/continuous.ex b/lib/exstatic/continuous_pdf.ex
similarity index 95%
rename from lib/exstatic/continuous.ex
rename to lib/exstatic/continuous_pdf.ex
index 4e8f2aa..c699f67 100644
--- a/lib/exstatic/continuous.ex
+++ b/lib/exstatic/continuous_pdf.ex
@@ -1,4 +1,4 @@
-defmodule Exstatic.Continuous do
+defmodule Exstatic.ContinuousPDF do
   @moduledoc """
   Defines the behaviour for continuous probability distributions that support 
   probability density function (PDF) calculations.
diff --git a/lib/exstatic/distribution/normal.ex b/lib/exstatic/distribution/normal.ex
index 5e06037..432817b 100644
--- a/lib/exstatic/distribution/normal.ex
+++ b/lib/exstatic/distribution/normal.ex
@@ -20,7 +20,7 @@ defmodule Exstatic.Distribution.Normal do
   """
 
   @behaviour Exstatic.Distribution
-  @behaviour Exstatic.Continuous
+  @behaviour Exstatic.ContinuousPDF
   @behaviour Exstatic.ContinuousCDF
 
   defstruct [:mean, :std_dev]
@@ -92,7 +92,7 @@ defmodule Exstatic.Distribution.Normal do
       iex> TestHelper.assert_in_delta(Normal.pdf(n, 0.0), 0.03989422804014326779399, 1.0e-17)
       true
   """
-  @impl Exstatic.Continuous
+  @impl Exstatic.ContinuousPDF
   def pdf(%__MODULE__{} = dist, x) when is_number(x) do
     Exstatic.Native.normal_pdf(dist.mean, dist.std_dev, x)
   end
@@ -274,7 +274,7 @@ defmodule Exstatic.Distribution.Normal do
       iex> TestHelper.assert_in_delta(result, -0.9189385332046727) # approximately -ln(√(2π))
       true
   """
-  @impl Exstatic.Continuous
+  @impl Exstatic.ContinuousPDF
   def ln_pdf(%__MODULE__{} = dist, x) when is_number(x) do
     Exstatic.Native.normal_ln_pdf(dist.mean, dist.std_dev, x)
   end
diff --git a/lib/exstatic/distribution/t.ex b/lib/exstatic/distribution/t.ex
index 7e17a9d..81bc1c8 100644
--- a/lib/exstatic/distribution/t.ex
+++ b/lib/exstatic/distribution/t.ex
@@ -22,7 +22,7 @@ defmodule Exstatic.Distribution.StandardizedT do
   """
 
   @behaviour Exstatic.Distribution
-  @behaviour Exstatic.Continuous
+  @behaviour Exstatic.ContinuousPDF
   @behaviour Exstatic.ContinuousCDF
 
   defstruct [:df]
@@ -98,7 +98,7 @@ defmodule Exstatic.Distribution.StandardizedT do
       iex> TestHelper.assert_in_delta(StandardizedT.pdf(t, 0.0), 0.37960669, 1.0e-6)
       true
   """
-  @impl Exstatic.Continuous
+  @impl Exstatic.ContinuousPDF
   def pdf(%__MODULE__{} = dist, x) when is_number(x) do
     Exstatic.Native.standardized_t_pdf(dist.df, x)
   end

From 1c434c9f6a85b443ebd90a2ac88a0aa6b6eb031b Mon Sep 17 00:00:00 2001
From: Brook <71849503+Primebrook@users.noreply.github.com>
Date: Thu, 6 Feb 2025 15:29:01 +0000
Subject: [PATCH 11/20] rename file

---
 lib/exstatic/distribution/{t.ex => standardized_t.ex} | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 rename lib/exstatic/distribution/{t.ex => standardized_t.ex} (100%)

diff --git a/lib/exstatic/distribution/t.ex b/lib/exstatic/distribution/standardized_t.ex
similarity index 100%
rename from lib/exstatic/distribution/t.ex
rename to lib/exstatic/distribution/standardized_t.ex

From 5a31ef691e4929616b13f929e8f78a1e49a7ada3 Mon Sep 17 00:00:00 2001
From: Brook <71849503+Primebrook@users.noreply.github.com>
Date: Thu, 6 Feb 2025 15:29:07 +0000
Subject: [PATCH 12/20] optional callbacks

---
 lib/exstatic/continuous_cdf.ex | 2 ++
 lib/exstatic/continuous_pdf.ex | 2 ++
 lib/exstatic/distribution.ex   | 2 ++
 3 files changed, 6 insertions(+)

diff --git a/lib/exstatic/continuous_cdf.ex b/lib/exstatic/continuous_cdf.ex
index b0148af..e109014 100644
--- a/lib/exstatic/continuous_cdf.ex
+++ b/lib/exstatic/continuous_cdf.ex
@@ -18,4 +18,6 @@ defmodule Exstatic.ContinuousCDF do
   @callback sf(distribution :: t(), x :: float()) :: float()
   @callback inverse_cdf(distribution :: t(), p :: float()) ::
               {:ok, float()} | {:error, :invalid_probability}
+
+  @optional_callbacks inverse_cdf: 2
 end
diff --git a/lib/exstatic/continuous_pdf.ex b/lib/exstatic/continuous_pdf.ex
index c699f67..daeaab7 100644
--- a/lib/exstatic/continuous_pdf.ex
+++ b/lib/exstatic/continuous_pdf.ex
@@ -17,4 +17,6 @@ defmodule Exstatic.ContinuousPDF do
 
   @callback pdf(distribution :: t(), x :: float()) :: float()
   @callback ln_pdf(distribution :: t(), x :: float()) :: float()
+
+  @optional_callbacks ln_pdf: 2
 end
diff --git a/lib/exstatic/distribution.ex b/lib/exstatic/distribution.ex
index 6c768a4..e471537 100644
--- a/lib/exstatic/distribution.ex
+++ b/lib/exstatic/distribution.ex
@@ -14,4 +14,6 @@ defmodule Exstatic.Distribution do
   @callback mode(distribution :: t()) :: float()
   @callback min(distribution :: t()) :: :neg_infinity | float()
   @callback max(distribution :: t()) :: :infinity | float()
+
+  @optional_callbacks std_dev: 1, entropy: 1, skewness: 1, median: 1, mode: 1, min: 1, max: 1
 end

From 3420af1c92c07bfa89bb3232d5dfdbd732bc8d2e Mon Sep 17 00:00:00 2001
From: Brook <71849503+Primebrook@users.noreply.github.com>
Date: Thu, 6 Feb 2025 15:33:49 +0000
Subject: [PATCH 13/20] credo

---
 .credo.exs         | 210 +++++++++++++++++++++++++++++++++++++++++++++
 .zed/settings.json |  15 ----
 2 files changed, 210 insertions(+), 15 deletions(-)
 create mode 100644 .credo.exs
 delete mode 100644 .zed/settings.json

diff --git a/.credo.exs b/.credo.exs
new file mode 100644
index 0000000..6e587fd
--- /dev/null
+++ b/.credo.exs
@@ -0,0 +1,210 @@
+# This file contains the configuration for Credo and you are probably reading
+# this after creating it with `mix credo.gen.config`.
+#
+# If you find anything wrong or unclear in this file, please report an
+# issue on GitHub: https://github.com/rrrene/credo/issues
+#
+%{
+  #
+  # You can have as many configs as you like in the `configs:` field.
+  configs: [
+    %{
+      #
+      # Run any config using `mix credo -C <name>`. If no config name is given
+      # "default" is used.
+      #
+      name: "default",
+      #
+      # These are the files included in the analysis:
+      files: %{
+        #
+        # You can give explicit globs or simply directories.
+        # In the latter case `**/*.{ex,exs}` will be used.
+        #
+        included: ["lib/", "test/"],
+        excluded: [
+          ~r"/_build/",
+          ~r"/deps/",
+          "test/support/"
+        ]
+      },
+      #
+      # Load and configure plugins here:
+      #
+      plugins: [],
+      #
+      # If you create your own checks, you must specify the source files for
+      # them here, so they can be loaded by Credo before running the analysis.
+      #
+      requires: [],
+      #
+      # If you want to enforce a style guide and need a more traditional linting
+      # experience, you can change `strict` to `true` below:
+      #
+      strict: true,
+      #
+      # To modify the timeout for parsing files, change this value:
+      #
+      parse_timeout: 5000,
+      #
+      # If you want to use uncolored output by default, you can change `color`
+      # to `false` below:
+      #
+      color: true,
+      #
+      # You can customize the parameters of any check by adding a second element
+      # to the tuple.
+      #
+      # To disable a check put `false` as second element:
+      #
+      #     {Credo.Check.Design.DuplicatedCode, false}
+      #
+      checks: %{
+        enabled: [
+          #
+          ## Consistency Checks
+          #
+          {Credo.Check.Consistency.ExceptionNames, []},
+          {Credo.Check.Consistency.LineEndings, []},
+          {Credo.Check.Consistency.MultiAliasImportRequireUse, []},
+          {Credo.Check.Consistency.ParameterPatternMatching, []},
+          {Credo.Check.Consistency.SpaceAroundOperators, []},
+          {Credo.Check.Consistency.SpaceInParentheses, []},
+          {Credo.Check.Consistency.TabsOrSpaces, [force: :spaces]},
+          {Credo.Check.Consistency.UnusedVariableNames, [force: :meaningful]},
+
+          #
+          ## Design Checks
+          #
+          # You can customize the priority of any check
+          # Priority values are: `low, normal, high, higher`
+          #
+          {Credo.Check.Design.AliasUsage,
+           [priority: :low, if_nested_deeper_than: 2, if_called_more_often_than: 0]},
+          # You can also customize the exit_status of each check.
+          # If you don't want TODO comments to cause `mix credo` to fail, just
+          # set this value to 0 (zero).
+          #
+          {Credo.Check.Design.TagTODO, [exit_status: 2]},
+          {Credo.Check.Design.TagFIXME, []},
+
+          #
+          ## Readability Checks
+          #
+          {Credo.Check.Readability.AliasOrder, []},
+          {Credo.Check.Readability.FunctionNames, []},
+          {Credo.Check.Readability.LargeNumbers, []},
+          {Credo.Check.Readability.MaxLineLength, [priority: :low, max_length: 120]},
+          {Credo.Check.Readability.ModuleAttributeNames, []},
+          {Credo.Check.Readability.ModuleDoc,
+           [
+             ignore_names:
+               ~r/(\.\w+Controller|\.Endpoint|\.\w+Live(\.\w+)?|\.Repo|\.Router|\.\w+Socket|\.\w+View|\.\w+Test|\.\w+Telemetry|\.\w+RecipeLive)$/
+           ]},
+          {Credo.Check.Readability.ModuleNames, []},
+          {Credo.Check.Readability.ParenthesesInCondition, []},
+          {Credo.Check.Readability.ParenthesesOnZeroArityDefs, []},
+          {Credo.Check.Readability.PipeIntoAnonymousFunctions, []},
+          {Credo.Check.Readability.PredicateFunctionNames, []},
+          {Credo.Check.Readability.PreferImplicitTry, []},
+          {Credo.Check.Readability.RedundantBlankLines, []},
+          {Credo.Check.Readability.Semicolons, []},
+          {Credo.Check.Readability.SpaceAfterCommas, []},
+          {Credo.Check.Readability.StrictModuleLayout,
+           [ignore_module_attributes: ~w/transform_description/a]},
+          {Credo.Check.Readability.StringSigils, []},
+          {Credo.Check.Readability.Specs, []},
+          {Credo.Check.Readability.TrailingBlankLine, []},
+          {Credo.Check.Readability.TrailingWhiteSpace, []},
+          {Credo.Check.Readability.UnnecessaryAliasExpansion, []},
+          {Credo.Check.Readability.VariableNames, []},
+          {Credo.Check.Readability.WithSingleClause, []},
+          {Credo.Check.Readability.ImplTrue, []},
+          {Credo.Check.Readability.SeparateAliasRequire, []},
+
+          #
+          ## Refactoring Opportunities
+          #
+          {Credo.Check.Refactor.Apply, []},
+          {Credo.Check.Refactor.CondStatements, []},
+          {Credo.Check.Refactor.CyclomaticComplexity, []},
+          {Credo.Check.Refactor.FunctionArity, []},
+          {Credo.Check.Refactor.LongQuoteBlocks, []},
+          {Credo.Check.Refactor.MatchInCondition, []},
+          {Credo.Check.Refactor.MapJoin, []},
+          {Credo.Check.Refactor.NegatedConditionsInUnless, []},
+          {Credo.Check.Refactor.NegatedConditionsWithElse, []},
+          {Credo.Check.Refactor.Nesting, []},
+          {Credo.Check.Refactor.UnlessWithElse, []},
+          {Credo.Check.Refactor.WithClauses, []},
+          {Credo.Check.Refactor.FilterFilter, []},
+          {Credo.Check.Refactor.RejectReject, []},
+          {Credo.Check.Refactor.RedundantWithClauseResult, []},
+
+          #
+          ## Warnings
+          #
+          {Credo.Check.Warning.ApplicationConfigInModuleAttribute, []},
+          {Credo.Check.Warning.BoolOperationOnSameValues, []},
+          {Credo.Check.Warning.ExpensiveEmptyEnumCheck, []},
+          {Credo.Check.Warning.IExPry, []},
+          {Credo.Check.Warning.IoInspect, []},
+          {Credo.Check.Warning.OperationOnSameValues, []},
+          {Credo.Check.Warning.OperationWithConstantResult, []},
+          {Credo.Check.Warning.RaiseInsideRescue, []},
+          {Credo.Check.Warning.SpecWithStruct, []},
+          {Credo.Check.Warning.WrongTestFileExtension, []},
+          {Credo.Check.Warning.UnusedEnumOperation, []},
+          {Credo.Check.Warning.UnusedFileOperation, []},
+          {Credo.Check.Warning.UnusedKeywordOperation, []},
+          {Credo.Check.Warning.UnusedListOperation, []},
+          {Credo.Check.Warning.UnusedPathOperation, []},
+          {Credo.Check.Warning.UnusedRegexOperation, []},
+          {Credo.Check.Warning.UnusedStringOperation, []},
+          {Credo.Check.Warning.UnusedTupleOperation, []},
+          {Credo.Check.Warning.UnsafeToAtom, []}
+        ],
+        disabled: [
+          #
+          # Checks scheduled for next check update (opt-in for now, just replace `false` with `[]`)
+
+          #
+          # Controversial and experimental checks (opt-in, just move the check to `:enabled`
+          #   and be sure to use `mix credo --strict` to see low priority checks)
+          #
+          {Credo.Check.Design.DuplicatedCode, []},
+          {Credo.Check.Design.SkipTestWithoutComment, []},
+          {Credo.Check.Readability.AliasAs, []},
+          {Credo.Check.Readability.BlockPipe, []},
+          {Credo.Check.Readability.MultiAlias, []},
+          {Credo.Check.Readability.NestedFunctionCalls, []},
+          {Credo.Check.Readability.SingleFunctionToBlockPipe, []},
+          {Credo.Check.Readability.SinglePipe, []},
+          {Credo.Check.Readability.WithCustomTaggedTuple, []},
+          {Credo.Check.Refactor.ABCSize, []},
+          {Credo.Check.Refactor.AppendSingleItem, []},
+          {Credo.Check.Refactor.DoubleBooleanNegation, []},
+          {Credo.Check.Refactor.FilterReject, []},
+          {Credo.Check.Refactor.IoPuts, []},
+          {Credo.Check.Refactor.MapMap, []},
+          {Credo.Check.Refactor.ModuleDependencies, []},
+          {Credo.Check.Refactor.NegatedIsNil, []},
+          {Credo.Check.Refactor.PipeChainStart, []},
+          {Credo.Check.Refactor.RejectFilter, []},
+          {Credo.Check.Refactor.VariableRebinding, []},
+          {Credo.Check.Warning.LazyLogging, []},
+          {Credo.Check.Warning.LeakyEnvironment, []},
+          {Credo.Check.Warning.MapGetUnsafePass, []},
+          {Credo.Check.Warning.MixEnv, []}
+
+          # {Credo.Check.Refactor.MapInto, []},
+
+          #
+          # Custom checks can be created using `mix credo.gen.check`.
+          #
+        ]
+      }
+    }
+  ]
+}
+
diff --git a/.zed/settings.json b/.zed/settings.json
deleted file mode 100644
index 7a5f440..0000000
--- a/.zed/settings.json
+++ /dev/null
@@ -1,15 +0,0 @@
-{
-  "lsp": {
-    "rust-analyzer": {
-      "binary": {
-        "ignore_system_version": true
-      },
-      "initialization_options": {
-        "linkedProjects": ["./native/exstatic/Cargo.toml"],
-        "rust": {
-          "analyzerTargetDir": true
-        }
-      }
-    }
-  }
-}

From e49c9f1beb9eb5e45e4c73699e785b7cc3610c83 Mon Sep 17 00:00:00 2001
From: Brook <71849503+Primebrook@users.noreply.github.com>
Date: Thu, 6 Feb 2025 15:37:47 +0000
Subject: [PATCH 14/20] dialyzer

---
 lib/exstatic/distribution/normal.ex         | 4 +++-
 lib/exstatic/distribution/standardized_t.ex | 2 ++
 test/test_helper.exs                        | 1 +
 3 files changed, 6 insertions(+), 1 deletion(-)

diff --git a/lib/exstatic/distribution/normal.ex b/lib/exstatic/distribution/normal.ex
index 432817b..1d3cccc 100644
--- a/lib/exstatic/distribution/normal.ex
+++ b/lib/exstatic/distribution/normal.ex
@@ -52,6 +52,7 @@ defmodule Exstatic.Distribution.Normal do
       iex> Normal.new(0.0, -1.0)
       {:error, :invalid_std_dev}
   """
+  @spec new(float(), float()) :: {:ok, t()} | {:error, :invalid_std_dev}
   def new(mean, std_dev) when is_number(mean) and is_number(std_dev) do
     if std_dev <= 0 do
       {:error, :invalid_std_dev}
@@ -63,7 +64,8 @@ defmodule Exstatic.Distribution.Normal do
   @doc """
   Creates a standard normal distribution with mean 0 and standard deviation 1.
   """
-  def standard(), do: %__MODULE__{mean: 0.0, std_dev: 1.0}
+  @spec standard() :: t()
+  def standard, do: %__MODULE__{mean: 0.0, std_dev: 1.0}
 
   @impl Exstatic.Distribution
   def mean(%__MODULE__{mean: mean}), do: mean
diff --git a/lib/exstatic/distribution/standardized_t.ex b/lib/exstatic/distribution/standardized_t.ex
index 81bc1c8..87023dc 100644
--- a/lib/exstatic/distribution/standardized_t.ex
+++ b/lib/exstatic/distribution/standardized_t.ex
@@ -47,6 +47,7 @@ defmodule Exstatic.Distribution.StandardizedT do
       iex> StandardizedT.new(-5.0)
       {:error, :invalid_df}
   """
+  @spec new(float()) :: {:ok, t()} | {:error, :invalid_df}
   def new(df) when is_number(df) and df > 1 do
     {:ok, %__MODULE__{df: df}}
   end
@@ -65,6 +66,7 @@ defmodule Exstatic.Distribution.StandardizedT do
       0.0
   """
   @impl Exstatic.Distribution
+  @spec mean(t) :: float()
   def mean(_t), do: 0.0
 
   @doc """
diff --git a/test/test_helper.exs b/test/test_helper.exs
index 2a7deed..048b64a 100644
--- a/test/test_helper.exs
+++ b/test/test_helper.exs
@@ -1,4 +1,5 @@
 defmodule TestHelper do
+  @spec assert_in_delta(number, number, number) :: boolean
   def assert_in_delta(actual, expected, delta \\ 1.0e-10) do
     abs(actual - expected) < delta
   end

From eb4120959cdaf7b7d9282d3a02b00bb8bbfcd37b Mon Sep 17 00:00:00 2001
From: Brook <71849503+Primebrook@users.noreply.github.com>
Date: Thu, 6 Feb 2025 15:51:29 +0000
Subject: [PATCH 15/20] specs for normal dist

---
 test/exstatic/distribution/normal_test.exs    | 139 ++++++++++++++++++
 .../{t_test.exs => standardized_t_test.exs}   |   0
 2 files changed, 139 insertions(+)
 rename test/exstatic/distribution/{t_test.exs => standardized_t_test.exs} (100%)

diff --git a/test/exstatic/distribution/normal_test.exs b/test/exstatic/distribution/normal_test.exs
index 6c014ab..ed94eb6 100644
--- a/test/exstatic/distribution/normal_test.exs
+++ b/test/exstatic/distribution/normal_test.exs
@@ -4,4 +4,143 @@ defmodule Exstatic.Distribution.NormalTest do
   alias Exstatic.Distribution.Normal
 
   doctest Exstatic.Distribution.Normal
+
+  describe "new/2" do
+    test "creates a valid normal distribution" do
+      assert {:ok, %Normal{mean: +0.0, std_dev: 1.0}} = Normal.new(0.0, 1.0)
+      assert {:ok, %Normal{mean: 10.0, std_dev: 2.5}} = Normal.new(10.0, 2.5)
+    end
+
+    test "returns an error for invalid standard deviation" do
+      assert {:error, :invalid_std_dev} = Normal.new(0.0, 0.0)
+      assert {:error, :invalid_std_dev} = Normal.new(0.0, -1.0)
+    end
+  end
+
+  describe "standard/0" do
+    test "returns a standard normal distribution (mean=0, std_dev=1)" do
+      dist = Normal.standard()
+      assert dist.mean == 0.0
+      assert dist.std_dev == 1.0
+    end
+  end
+
+  describe "mean/1" do
+    test "returns the mean of the distribution" do
+      {:ok, dist} = Normal.new(5.0, 1.0)
+      assert Normal.mean(dist) == 5.0
+    end
+  end
+
+  describe "std_dev/1" do
+    test "returns the standard deviation of the distribution" do
+      {:ok, dist} = Normal.new(5.0, 2.0)
+      assert Normal.std_dev(dist) == 2.0
+    end
+  end
+
+  describe "variance/1" do
+    test "computes the variance correctly" do
+      {:ok, dist} = Normal.new(0.0, 1.0)
+      assert Normal.variance(dist) == 1.0
+
+      {:ok, dist} = Normal.new(0.0, 2.0)
+      assert Normal.variance(dist) == 4.0
+
+      {:ok, dist} = Normal.new(0.0, 0.1)
+      assert TestHelper.assert_in_delta(Normal.variance(dist), 0.01)
+    end
+  end
+
+  describe "entropy/1" do
+    test "computes the entropy correctly" do
+      {:ok, dist} = Normal.new(0.0, 1.0)
+      assert TestHelper.assert_in_delta(Normal.entropy(dist), 1.41893853320467274178, 1.0e-15)
+
+      {:ok, dist} = Normal.new(0.0, 10.0)
+      assert TestHelper.assert_in_delta(Normal.entropy(dist), 3.721523626198718425798, 1.0e-15)
+    end
+  end
+
+  describe "skewness/1" do
+    test "returns 0 for normal distributions" do
+      {:ok, dist} = Normal.new(0.0, 1.0)
+      assert Normal.skewness(dist) == 0.0
+    end
+  end
+
+  describe "median/1" do
+    test "returns the mean as the median" do
+      {:ok, dist} = Normal.new(0.0, 1.0)
+      assert Normal.median(dist) == 0.0
+
+      {:ok, dist} = Normal.new(5.0, 1.0)
+      assert Normal.median(dist) == 5.0
+    end
+  end
+
+  describe "mode/1" do
+    test "returns the mean as the mode" do
+      {:ok, dist} = Normal.new(0.0, 1.0)
+      assert Normal.mode(dist) == 0.0
+
+      {:ok, dist} = Normal.new(5.0, 2.0)
+      assert Normal.mode(dist) == 5.0
+    end
+  end
+
+  describe "min/1 and max/1" do
+    test "returns negative and positive infinity respectively" do
+      {:ok, dist} = Normal.new(0.0, 1.0)
+      assert Normal.min(dist) == :neg_infinity
+      assert Normal.max(dist) == :infinity
+    end
+  end
+
+  describe "pdf/2" do
+    test "computes valid probability density function (PDF) values" do
+      {:ok, dist} = Normal.new(0.0, 1.0)
+      assert TestHelper.assert_in_delta(Normal.pdf(dist, 0.0), 0.3989422804014327, 1.0e-15)
+      assert TestHelper.assert_in_delta(Normal.pdf(dist, 1.0), 0.24197072451914337, 1.0e-15)
+      assert TestHelper.assert_in_delta(Normal.pdf(dist, -1.0), 0.24197072451914337, 1.0e-15)
+    end
+  end
+
+  describe "cdf/2" do
+    test "computes valid cumulative distribution function (CDF) values" do
+      {:ok, dist} = Normal.new(0.0, 1.0)
+      assert TestHelper.assert_in_delta(Normal.cdf(dist, 0.0), 0.5, 1.0e-9)
+      assert TestHelper.assert_in_delta(Normal.cdf(dist, -5.0), 0.0000002866515718, 1.0e-16)
+      assert TestHelper.assert_in_delta(Normal.cdf(dist, 5.0), 0.9999997133484281, 1.0e-16)
+    end
+  end
+
+  describe "sf/2" do
+    test "computes valid survival function (SF) values" do
+      {:ok, dist} = Normal.new(0.0, 1.0)
+      assert TestHelper.assert_in_delta(Normal.sf(dist, 0.0), 0.5, 1.0e-9)
+      assert TestHelper.assert_in_delta(Normal.sf(dist, -5.0), 0.9999997133484281, 1.0e-16)
+      assert TestHelper.assert_in_delta(Normal.sf(dist, 5.0), 0.0000002866515718, 1.0e-16)
+    end
+  end
+
+  describe "ln_pdf/2" do
+    test "computes the log probability density function (ln(PDF))" do
+      {:ok, dist} = Normal.new(0.0, 1.0)
+      expected_ln_pdf = -0.9189385332046727
+      assert TestHelper.assert_in_delta(Normal.ln_pdf(dist, 0.0), expected_ln_pdf, 1.0e-9)
+    end
+  end
+
+  describe "inverse_cdf/2" do
+    test "computes the inverse CDF (quantile function) correctly" do
+      {:ok, dist} = Normal.new(0.0, 1.0)
+
+      assert {:ok, result} = Normal.inverse_cdf(dist, 0.975)
+      assert TestHelper.assert_in_delta(result, 1.959963984540054, 1.0e-9)
+
+      assert {:error, :invalid_probability} = Normal.inverse_cdf(dist, -0.1)
+      assert {:error, :invalid_probability} = Normal.inverse_cdf(dist, 1.5)
+    end
+  end
 end
diff --git a/test/exstatic/distribution/t_test.exs b/test/exstatic/distribution/standardized_t_test.exs
similarity index 100%
rename from test/exstatic/distribution/t_test.exs
rename to test/exstatic/distribution/standardized_t_test.exs

From 19e2b3fea8bc39b3fdf19d647b183eba68425d77 Mon Sep 17 00:00:00 2001
From: Brook <71849503+Primebrook@users.noreply.github.com>
Date: Thu, 6 Feb 2025 16:00:20 +0000
Subject: [PATCH 16/20] ignore Rust NIF calls in test coverage

---
 mix.exs | 8 +++++++-
 1 file changed, 7 insertions(+), 1 deletion(-)

diff --git a/mix.exs b/mix.exs
index fc778f1..b54c898 100644
--- a/mix.exs
+++ b/mix.exs
@@ -17,7 +17,13 @@ defmodule Exstatic.MixProject do
       docs: docs(),
       package: package(),
       name: "Exstatic",
-      source_url: @source_url
+      source_url: @source_url,
+      test_coverage: [
+        summary: [threshold: 90],
+        ignore_modules: [
+          Exstatic.Native
+        ]
+      ]
     ]
   end
 

From b2152834d497e44fd6a605f295f9a492cc365d1e Mon Sep 17 00:00:00 2001
From: Brook <71849503+Primebrook@users.noreply.github.com>
Date: Thu, 6 Feb 2025 16:02:00 +0000
Subject: [PATCH 17/20] delete vscode config

---
 .vscode/settings.json | 3 ---
 1 file changed, 3 deletions(-)
 delete mode 100644 .vscode/settings.json

diff --git a/.vscode/settings.json b/.vscode/settings.json
deleted file mode 100644
index b44cc34..0000000
--- a/.vscode/settings.json
+++ /dev/null
@@ -1,3 +0,0 @@
-{
-  "rust-analyzer.linkedProjects": ["native/exstatic/Cargo.toml"]
-}

From fe4204790721267b6f15ed1989322e5915ae92b2 Mon Sep 17 00:00:00 2001
From: Brook <71849503+Primebrook@users.noreply.github.com>
Date: Thu, 6 Feb 2025 16:09:13 +0000
Subject: [PATCH 18/20] sobelow

---
 mix.exs  | 3 ++-
 mix.lock | 1 +
 2 files changed, 3 insertions(+), 1 deletion(-)

diff --git a/mix.exs b/mix.exs
index b54c898..5ee458f 100644
--- a/mix.exs
+++ b/mix.exs
@@ -73,7 +73,8 @@ defmodule Exstatic.MixProject do
       {:rustler, "~> 0.35.1", runtime: false},
       {:credo, "~> 1.7", only: [:dev, :test], runtime: false},
       {:dialyxir, "~> 1.4", only: [:dev, :test], runtime: false},
-      {:ex_doc, "~> 0.34", only: :dev, runtime: false}
+      {:ex_doc, "~> 0.34", only: :dev, runtime: false},
+      {:sobelow, "~> 0.13", only: [:dev, :test], runtime: false}
     ]
   end
 end
diff --git a/mix.lock b/mix.lock
index 74689b0..ff0a6bb 100644
--- a/mix.lock
+++ b/mix.lock
@@ -19,6 +19,7 @@
   "nimble_pool": {:hex, :nimble_pool, "1.1.0", "bf9c29fbdcba3564a8b800d1eeb5a3c58f36e1e11d7b7fb2e084a643f645f06b", [:mix], [], "hexpm", "af2e4e6b34197db81f7aad230c1118eac993acc0dae6bc83bac0126d4ae0813a"},
   "req": {:hex, :req, "0.5.8", "50d8d65279d6e343a5e46980ac2a70e97136182950833a1968b371e753f6a662", [:mix], [{:brotli, "~> 0.3.1", [hex: :brotli, repo: "hexpm", optional: true]}, {:ezstd, "~> 1.0", [hex: :ezstd, repo: "hexpm", optional: true]}, {:finch, "~> 0.17", [hex: :finch, repo: "hexpm", optional: false]}, {:jason, "~> 1.0", [hex: :jason, repo: "hexpm", optional: false]}, {:mime, "~> 2.0.6 or ~> 2.1", [hex: :mime, repo: "hexpm", optional: false]}, {:nimble_csv, "~> 1.0", [hex: :nimble_csv, repo: "hexpm", optional: true]}, {:plug, "~> 1.0", [hex: :plug, repo: "hexpm", optional: true]}], "hexpm", "d7fc5898a566477e174f26887821a3c5082b243885520ee4b45555f5d53f40ef"},
   "rustler": {:hex, :rustler, "0.35.1", "ec81961ef9ee833d721dafb4449cab29b16b969a3063a842bb9e3ea912f6b938", [:mix], [{:jason, "~> 1.0", [hex: :jason, repo: "hexpm", optional: false]}, {:req, "~> 0.5", [hex: :req, repo: "hexpm", optional: false]}, {:toml, "~> 0.6", [hex: :toml, repo: "hexpm", optional: false]}], "hexpm", "3713b2e70e68ec2bfa8291dfd9cb811fe64a770f254cd9c331f8b34fa7989115"},
+  "sobelow": {:hex, :sobelow, "0.13.0", "218afe9075904793f5c64b8837cc356e493d88fddde126a463839351870b8d1e", [:mix], [{:jason, "~> 1.0", [hex: :jason, repo: "hexpm", optional: false]}], "hexpm", "cd6e9026b85fc35d7529da14f95e85a078d9dd1907a9097b3ba6ac7ebbe34a0d"},
   "telemetry": {:hex, :telemetry, "1.3.0", "fedebbae410d715cf8e7062c96a1ef32ec22e764197f70cda73d82778d61e7a2", [:rebar3], [], "hexpm", "7015fc8919dbe63764f4b4b87a95b7c0996bd539e0d499be6ec9d7f3875b79e6"},
   "toml": {:hex, :toml, "0.7.0", "fbcd773caa937d0c7a02c301a1feea25612720ac3fa1ccb8bfd9d30d822911de", [:mix], [], "hexpm", "0690246a2478c1defd100b0c9b89b4ea280a22be9a7b313a8a058a2408a2fa70"},
 }

From 489260fc13da262369a4394c858ea5f34186436b Mon Sep 17 00:00:00 2001
From: Brook <71849503+Primebrook@users.noreply.github.com>
Date: Thu, 6 Feb 2025 16:24:47 +0000
Subject: [PATCH 19/20] elixir wrapper module should not be referenced directly

---
 lib/exstatic/distribution/standardized_t.ex | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/exstatic/distribution/standardized_t.ex b/lib/exstatic/distribution/standardized_t.ex
index 87023dc..802a86c 100644
--- a/lib/exstatic/distribution/standardized_t.ex
+++ b/lib/exstatic/distribution/standardized_t.ex
@@ -73,7 +73,7 @@ defmodule Exstatic.Distribution.StandardizedT do
   Returns the variance of the t-distribution.
 
   - If `1 < df ≤ 2`, the variance is `:infinity`.
-  - Otherwise, the variance is computed using `Exstatic.Native.standardized_t_variance/1`.
+  - Otherwise, the variance is computed using the native Rust implementation.
 
   ## Examples
 

From c034edb1fe165a9a2784c4941d36c198a1091c41 Mon Sep 17 00:00:00 2001
From: Brook <71849503+Primebrook@users.noreply.github.com>
Date: Thu, 6 Feb 2025 16:42:11 +0000
Subject: [PATCH 20/20] update package and docs links

---
 README.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/README.md b/README.md
index 66ef0d5..40c308f 100644
--- a/README.md
+++ b/README.md
@@ -1,7 +1,7 @@
 # Exstatic
 
-[![Hex.pm](https://img.shields.io/hexpm/v/exstatic.svg)](https://hex.pm/packages/exstatic)
-[![Docs](https://img.shields.io/badge/hex-docs-blue.svg)](https://hexdocs.pm/exstatic)
+[![Hex.pm](https://img.shields.io/hexpm/v/exstatic.svg)](https://hex.pm/packages/zappi/exstatic)
+[![Docs](https://img.shields.io/badge/hex-docs-blue.svg)](https://zappi.hexdocs.pm/exstatic)
 
 Exstatic provides idiomatic Elixir interfaces for working with statistical distributions. Built on top of the battle-tested [statrs](https://docs.rs/statrs) Rust library, it combines Elixir's elegant syntax with Rust's numerical computing capabilities.