From a32a4515c1dae2cc1abaee447cabc01dda7568a4 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jakub=20=C5=9Al=C4=99zak?=
 <128084860+jaksle@users.noreply.github.com>
Date: Wed, 3 Dec 2025 21:50:37 +0100
Subject: [PATCH 01/15] Update cosine.jl

---
 src/univariate/continuous/cosine.jl | 18 ++++++++++++++++++
 1 file changed, 18 insertions(+)

diff --git a/src/univariate/continuous/cosine.jl b/src/univariate/continuous/cosine.jl
index 4d11a9ddde..9c9e17fe7a 100644
--- a/src/univariate/continuous/cosine.jl
+++ b/src/univariate/continuous/cosine.jl
@@ -93,3 +93,21 @@ function ccdf(d::Cosine{T}, x::Real) where T<:Real
 end
 
 quantile(d::Cosine, p::Real) = quantile_bisect(d, p)
+
+function mgf(d::Cosine, t::Real)
+    μ, σ = params(d)
+    return π^2 * exp(μ*t) * sinh(σ*t) / (σ*t*(π^2 + (σ*t)^2))
+end
+
+function cgf(d::Cosine{T}, t) where T<:Real
+    μ, σ = params(d)
+    t ≈ 0. && return one(complex(T))
+    σ*abs(t) ≈ π && return cis(μ*t) / 2
+
+    return π^2 * cis(μ*t) * sin(σ*t) / (σ*t*(π^2 - (σ*t)^2))
+end
+
+#### Affine transformations
+
+Base.:+(d::Cosine, a::Real) = Cosine(d.μ + a, d.σ)
+Base.:*(c::Real, d::Cosine) = Cosine(c * d.μ, abs(c) * d.σ)

From 0ef458c8c209d820923b0ce2d09a33cd25f176f2 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jakub=20=C5=9Al=C4=99zak?=
 <128084860+jaksle@users.noreply.github.com>
Date: Wed, 3 Dec 2025 22:09:05 +0100
Subject: [PATCH 02/15] Update cosine.jl

---
 src/univariate/continuous/cosine.jl | 1 +
 1 file changed, 1 insertion(+)

diff --git a/src/univariate/continuous/cosine.jl b/src/univariate/continuous/cosine.jl
index 9c9e17fe7a..3294f9320f 100644
--- a/src/univariate/continuous/cosine.jl
+++ b/src/univariate/continuous/cosine.jl
@@ -96,6 +96,7 @@ quantile(d::Cosine, p::Real) = quantile_bisect(d, p)
 
 function mgf(d::Cosine, t::Real)
     μ, σ = params(d)
+    t ≈ 0. && return exp(μ*t)
     return π^2 * exp(μ*t) * sinh(σ*t) / (σ*t*(π^2 + (σ*t)^2))
 end
 

From 9739851afc9541cab38fe084ab96c8137b27bfab Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jakub=20=C5=9Al=C4=99zak?=
 <128084860+jaksle@users.noreply.github.com>
Date: Wed, 3 Dec 2025 22:10:36 +0100
Subject: [PATCH 03/15] Update cosine.jl

---
 src/univariate/continuous/cosine.jl | 1 -
 1 file changed, 1 deletion(-)

diff --git a/src/univariate/continuous/cosine.jl b/src/univariate/continuous/cosine.jl
index 3294f9320f..16d8df3054 100644
--- a/src/univariate/continuous/cosine.jl
+++ b/src/univariate/continuous/cosine.jl
@@ -104,7 +104,6 @@ function cgf(d::Cosine{T}, t) where T<:Real
     μ, σ = params(d)
     t ≈ 0. && return one(complex(T))
     σ*abs(t) ≈ π && return cis(μ*t) / 2
-
     return π^2 * cis(μ*t) * sin(σ*t) / (σ*t*(π^2 - (σ*t)^2))
 end
 

From e7f7d4526038cc1aab73f28dd0ddf226f6dc786c Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jakub=20=C5=9Al=C4=99zak?=
 <128084860+jaksle@users.noreply.github.com>
Date: Wed, 3 Dec 2025 22:35:57 +0100
Subject: [PATCH 04/15] Update cosine.jl

---
 src/univariate/continuous/cosine.jl | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/src/univariate/continuous/cosine.jl b/src/univariate/continuous/cosine.jl
index 16d8df3054..bd37564824 100644
--- a/src/univariate/continuous/cosine.jl
+++ b/src/univariate/continuous/cosine.jl
@@ -94,17 +94,17 @@ end
 
 quantile(d::Cosine, p::Real) = quantile_bisect(d, p)
 
-function mgf(d::Cosine, t::Real)
+function mgf(d::Cosine{T}, t::Real) where T<:Real
     μ, σ = params(d)
     t ≈ 0. && return exp(μ*t)
-    return π^2 * exp(μ*t) * sinh(σ*t) / (σ*t*(π^2 + (σ*t)^2))
+    return T(π^2) * exp(μ*t) * sinh(σ*t) / (σ*t*(T(π^2) + (σ*t)^2))
 end
 
-function cgf(d::Cosine{T}, t) where T<:Real
+function cf(d::Cosine{T}, t::Real) where T<:Real
     μ, σ = params(d)
     t ≈ 0. && return one(complex(T))
     σ*abs(t) ≈ π && return cis(μ*t) / 2
-    return π^2 * cis(μ*t) * sin(σ*t) / (σ*t*(π^2 - (σ*t)^2))
+    return T(π)^2 * cis(μ*t) * sin(σ*t) / (σ*t*(T(π)^2 - (σ*t)^2))
 end
 
 #### Affine transformations

From c687dbbe71474d71436b5088b14e52e0f61dc86e Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jakub=20=C5=9Al=C4=99zak?=
 <128084860+jaksle@users.noreply.github.com>
Date: Thu, 4 Dec 2025 19:48:55 +0100
Subject: [PATCH 05/15] add cgf

---
 src/univariate/continuous/cosine.jl | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/src/univariate/continuous/cosine.jl b/src/univariate/continuous/cosine.jl
index bd37564824..1bf536b975 100644
--- a/src/univariate/continuous/cosine.jl
+++ b/src/univariate/continuous/cosine.jl
@@ -100,6 +100,12 @@ function mgf(d::Cosine{T}, t::Real) where T<:Real
     return T(π^2) * exp(μ*t) * sinh(σ*t) / (σ*t*(T(π^2) + (σ*t)^2))
 end
 
+function cgf(d::Cosine{T}, t::Real) where T<:Real
+    μ, σ = params(d)
+    t ≈ 0. && return μ*t
+    return 2log(π) + μ*t + σ*abs(t) + log1p(-exp(-2σ*abs(t))) - log(2) - log(σ*abs(t)) - log(T(π^2) + (σ*t)^2)
+end
+
 function cf(d::Cosine{T}, t::Real) where T<:Real
     μ, σ = params(d)
     t ≈ 0. && return one(complex(T))

From 1d43ceadbb73736b57a87cd90e0095b61544a7d3 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jakub=20=C5=9Al=C4=99zak?=
 <128084860+jaksle@users.noreply.github.com>
Date: Thu, 4 Dec 2025 22:27:42 +0100
Subject: [PATCH 06/15] Update src/univariate/continuous/cosine.jl
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

Co-authored-by: David Müller-Widmann <devmotion@users.noreply.github.com>
---
 src/univariate/continuous/cosine.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/univariate/continuous/cosine.jl b/src/univariate/continuous/cosine.jl
index 1bf536b975..c549f4ad34 100644
--- a/src/univariate/continuous/cosine.jl
+++ b/src/univariate/continuous/cosine.jl
@@ -95,7 +95,7 @@ end
 quantile(d::Cosine, p::Real) = quantile_bisect(d, p)
 
 function mgf(d::Cosine{T}, t::Real) where T<:Real
-    μ, σ = params(d)
+    (; μ, σ) = d
     t ≈ 0. && return exp(μ*t)
     return T(π^2) * exp(μ*t) * sinh(σ*t) / (σ*t*(T(π^2) + (σ*t)^2))
 end

From ccae0fb5014c148cfbd5fb5d100c7ee2d398520b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jakub=20=C5=9Al=C4=99zak?=
 <128084860+jaksle@users.noreply.github.com>
Date: Thu, 4 Dec 2025 22:28:19 +0100
Subject: [PATCH 07/15] Update src/univariate/continuous/cosine.jl
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

Co-authored-by: David Müller-Widmann <devmotion@users.noreply.github.com>
---
 src/univariate/continuous/cosine.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/univariate/continuous/cosine.jl b/src/univariate/continuous/cosine.jl
index c549f4ad34..e910e74de6 100644
--- a/src/univariate/continuous/cosine.jl
+++ b/src/univariate/continuous/cosine.jl
@@ -94,7 +94,7 @@ end
 
 quantile(d::Cosine, p::Real) = quantile_bisect(d, p)
 
-function mgf(d::Cosine{T}, t::Real) where T<:Real
+function mgf(d::Cosine, t::Real)
     (; μ, σ) = d
     t ≈ 0. && return exp(μ*t)
     return T(π^2) * exp(μ*t) * sinh(σ*t) / (σ*t*(T(π^2) + (σ*t)^2))

From 58a05996249c338b73fb44ac32037e416cc8d8f2 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jakub=20=C5=9Al=C4=99zak?=
 <128084860+jaksle@users.noreply.github.com>
Date: Thu, 4 Dec 2025 22:28:56 +0100
Subject: [PATCH 08/15] Update src/univariate/continuous/cosine.jl
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

Co-authored-by: David Müller-Widmann <devmotion@users.noreply.github.com>
---
 src/univariate/continuous/cosine.jl | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/src/univariate/continuous/cosine.jl b/src/univariate/continuous/cosine.jl
index e910e74de6..8911c020c5 100644
--- a/src/univariate/continuous/cosine.jl
+++ b/src/univariate/continuous/cosine.jl
@@ -96,8 +96,9 @@ quantile(d::Cosine, p::Real) = quantile_bisect(d, p)
 
 function mgf(d::Cosine, t::Real)
     (; μ, σ) = d
-    t ≈ 0. && return exp(μ*t)
-    return T(π^2) * exp(μ*t) * sinh(σ*t) / (σ*t*(T(π^2) + (σ*t)^2))
+    σt = σ * t
+    z = iszero(σt) ? one(float(σt)) : sinh(σ*t)/(σ*t)
+    return exp(μ*t) * (z / (1 + (IrrationalConstants.invπ * σt)^2))
 end
 
 function cgf(d::Cosine{T}, t::Real) where T<:Real

From e688e375271d5a2d8df903e227677ddc5023965a Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jakub=20=C5=9Al=C4=99zak?=
 <128084860+jaksle@users.noreply.github.com>
Date: Thu, 4 Dec 2025 22:29:36 +0100
Subject: [PATCH 09/15] Update src/univariate/continuous/cosine.jl
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

Co-authored-by: David Müller-Widmann <devmotion@users.noreply.github.com>
---
 src/univariate/continuous/cosine.jl | 9 +++++----
 1 file changed, 5 insertions(+), 4 deletions(-)

diff --git a/src/univariate/continuous/cosine.jl b/src/univariate/continuous/cosine.jl
index 8911c020c5..ceaa062101 100644
--- a/src/univariate/continuous/cosine.jl
+++ b/src/univariate/continuous/cosine.jl
@@ -101,10 +101,11 @@ function mgf(d::Cosine, t::Real)
     return exp(μ*t) * (z / (1 + (IrrationalConstants.invπ * σt)^2))
 end
 
-function cgf(d::Cosine{T}, t::Real) where T<:Real
-    μ, σ = params(d)
-    t ≈ 0. && return μ*t
-    return 2log(π) + μ*t + σ*abs(t) + log1p(-exp(-2σ*abs(t))) - log(2) - log(σ*abs(t)) - log(T(π^2) + (σ*t)^2)
+function cgf(d::Cosine, t::Real)
+    (; μ, σ) = d
+    σt = σ * t
+    z = iszero(σt) ? zero(float(σt)) : LogExpFunctions.logabssinh(σt) - log(σt)
+    return μ*t + z - LogExpFunctions.log1psq(invπ * σt)
 end
 
 function cf(d::Cosine{T}, t::Real) where T<:Real

From 430e71395c2dd3857330224ab8f45293fbf01e0c Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jakub=20=C5=9Al=C4=99zak?=
 <128084860+jaksle@users.noreply.github.com>
Date: Thu, 4 Dec 2025 23:12:02 +0100
Subject: [PATCH 10/15] Update cosine.jl

---
 src/univariate/continuous/cosine.jl | 46 ++++++++++++++++-------------
 1 file changed, 25 insertions(+), 21 deletions(-)

diff --git a/src/univariate/continuous/cosine.jl b/src/univariate/continuous/cosine.jl
index ceaa062101..d9dc788210 100644
--- a/src/univariate/continuous/cosine.jl
+++ b/src/univariate/continuous/cosine.jl
@@ -59,34 +59,37 @@ kurtosis(d::Cosine{T}) where {T<:Real} = 6*(90-T(π)^4) / (5*(T(π)^2-6)^2)
 
 #### Evaluation
 
-function pdf(d::Cosine{T}, x::Real) where T<:Real
+function pdf(d::Cosine{T}, x::S) where {T<:Real, S<:Real}
+    W = promote_type(T, S)
     if insupport(d, x)
         z = (x - d.μ) / d.σ
         return (1 + cospi(z)) / (2d.σ)
     else
-        return zero(T)
+        return zero(W)
     end
 end
 
 logpdf(d::Cosine, x::Real) = log(pdf(d, x))
 
-function cdf(d::Cosine{T}, x::Real) where T<:Real
+function cdf(d::Cosine{T}, x::S) where {T<:Real, S<:Real}
+    W = promote_type(T, S)
     if x < d.μ - d.σ
-        return zero(T)
+        return zero(W)
     end
     if x > d.μ + d.σ
-        return one(T)
+        return one(W)
     end
     z = (x - d.μ) / d.σ
     (1 + z + sinpi(z) * invπ) / 2
 end
 
-function ccdf(d::Cosine{T}, x::Real) where T<:Real
+function cdf(d::Cosine{T}, x::S) where {T<:Real, S<:Real}
+    W = promote_type(T, S)
     if x < d.μ - d.σ
-        return one(T)
+        return one(W)
     end
     if x > d.μ + d.σ
-        return zero(T)
+        return zero(W)
     end
     nz = (d.μ - x) / d.σ
     (1 + nz + sinpi(nz) * invπ) / 2
@@ -94,25 +97,26 @@ end
 
 quantile(d::Cosine, p::Real) = quantile_bisect(d, p)
 
+import IrrationalConstants: invπ
+import LogExpFunctions: logabssinh, log1psq
+
 function mgf(d::Cosine, t::Real)
-    (; μ, σ) = d
-    σt = σ * t
-    z = iszero(σt) ? one(float(σt)) : sinh(σ*t)/(σ*t)
-    return exp(μ*t) * (z / (1 + (IrrationalConstants.invπ * σt)^2))
+    σt, μt = d.σ * t, d.μ*t
+    z = iszero(σt) ? one(float(σt)) : sinh(σt)/σt
+    return exp(μt) * (z / (1 + (invπ * σt)^2))
 end
 
 function cgf(d::Cosine, t::Real)
-    (; μ, σ) = d
-    σt = σ * t
-    z = iszero(σt) ? zero(float(σt)) : LogExpFunctions.logabssinh(σt) - log(σt)
-    return μ*t + z - LogExpFunctions.log1psq(invπ * σt)
+    σt, μt = d.σ * t, d.μ*t
+    z = iszero(σt) ? zero(float(σt)) : logabssinh(σt) - log(σt)
+    return μt + z - log1psq(invπ * σt)
 end
 
-function cf(d::Cosine{T}, t::Real) where T<:Real
-    μ, σ = params(d)
-    t ≈ 0. && return one(complex(T))
-    σ*abs(t) ≈ π && return cis(μ*t) / 2
-    return T(π)^2 * cis(μ*t) * sin(σ*t) / (σ*t*(T(π)^2 - (σ*t)^2))
+function cf(d::Cosine, t::Real)
+    σt, μt = d.σ * t, d.μ*t
+    abs(σt) ≈ π && return cis(μt) / 2
+    z = iszero(σt) ? one(float(σt)) : sin(σt)/σt
+    return π^2 * cis(μt) * z / (π^2 - (σt)^2)
 end
 
 #### Affine transformations

From 10394b93dd4c4176779cfebfad0b7d9f2a425401 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jakub=20=C5=9Al=C4=99zak?=
 <128084860+jaksle@users.noreply.github.com>
Date: Fri, 5 Dec 2025 00:13:34 +0100
Subject: [PATCH 11/15] test + dependencies

---
 src/Distributions.jl | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/src/Distributions.jl b/src/Distributions.jl
index fcf6994347..b0d540fdb8 100644
--- a/src/Distributions.jl
+++ b/src/Distributions.jl
@@ -25,8 +25,9 @@ import StatsBase: kurtosis, skewness, entropy, mode, modes,
 import PDMats: dim, PDMat, invquad
 
 using SpecialFunctions
+import LogExpFunctions: logabssinh, log1psq
 using Base.MathConstants: eulergamma
-
+import IrrationalConstants: invπ
 import AliasTables
 
 export

From 2c4edb5d6b8522b6beb44d56a8a437e8f615b12e Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jakub=20=C5=9Al=C4=99zak?=
 <128084860+jaksle@users.noreply.github.com>
Date: Fri, 5 Dec 2025 00:15:58 +0100
Subject: [PATCH 12/15] test + dependencies

---
 Project.toml                         |  4 ++++
 test/univariate/continuous/cosine.jl | 13 +++++++++++++
 2 files changed, 17 insertions(+)
 create mode 100644 test/univariate/continuous/cosine.jl

diff --git a/Project.toml b/Project.toml
index 643ea0f47e..e4bf95ef41 100644
--- a/Project.toml
+++ b/Project.toml
@@ -9,6 +9,8 @@ ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
 DensityInterface = "b429d917-457f-4dbc-8f4c-0cc954292b1d"
 FillArrays = "1a297f60-69ca-5386-bcde-b61e274b549b"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+LogExpFunctions = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
+IrrationalConstants = "92d709cd-6900-40b7-9082-c6be49f344b6"
 PDMats = "90014a1f-27ba-587c-ab20-58faa44d9150"
 Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7"
 QuadGK = "1fd47b50-473d-5c70-9696-f719f8f3bcdc"
@@ -43,6 +45,8 @@ FiniteDifferences = "0.12"
 ForwardDiff = "0.10, 1"
 JSON = "0.21"
 LinearAlgebra = "<0.0.1, 1"
+LogExpFunctions = "0.3.29"
+IrrationalConstants = "0.2.6"
 OffsetArrays = "1"
 PDMats = "0.11.35"
 Printf = "<0.0.1, 1"
diff --git a/test/univariate/continuous/cosine.jl b/test/univariate/continuous/cosine.jl
new file mode 100644
index 0000000000..db4496fe19
--- /dev/null
+++ b/test/univariate/continuous/cosine.jl
@@ -0,0 +1,13 @@
+@testset "Cosine" begin
+    @testset "mgf, cgf, cf" begin
+        @test cf(Cosine(1, 1), 1) ≈ cis(1) * sin(1)/(1 - π^-2)
+        @test mgf(Cosine(-1, 2), -1) ≈ exp(1) * sinh(-2) / (-2*(1 + 4π^-2))
+        @test cgf(Cosine(-1, 2), 2) ≈ -2 + log(sinh(4)) - log(4) - log(1 + 16π^-2)
+    end
+
+    @testset "affine transfomations" begin
+        @test -Cosine(1, 1) == Cosine(-1, 1)
+        @test 3Cosine(1, 2) == Cosine(3, 6)
+        @test Cosine(0, 2) + 42 == Cosine(42, 2)
+    end
+end
\ No newline at end of file

From ce1016e22c7445f2a79212f156a55c5cf81e6133 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jakub=20=C5=9Al=C4=99zak?=
 <128084860+jaksle@users.noreply.github.com>
Date: Fri, 5 Dec 2025 00:47:51 +0100
Subject: [PATCH 13/15] logpdf + tweaks

---
 src/univariate/continuous/cosine.jl | 37 ++++++++++++++---------------
 1 file changed, 18 insertions(+), 19 deletions(-)

diff --git a/src/univariate/continuous/cosine.jl b/src/univariate/continuous/cosine.jl
index d9dc788210..e2d4b712f7 100644
--- a/src/univariate/continuous/cosine.jl
+++ b/src/univariate/continuous/cosine.jl
@@ -60,46 +60,45 @@ kurtosis(d::Cosine{T}) where {T<:Real} = 6*(90-T(π)^4) / (5*(T(π)^2-6)^2)
 #### Evaluation
 
 function pdf(d::Cosine{T}, x::S) where {T<:Real, S<:Real}
-    W = promote_type(T, S)
     if insupport(d, x)
         z = (x - d.μ) / d.σ
         return (1 + cospi(z)) / (2d.σ)
     else
-        return zero(W)
+        return zero(promote_type(T, S))
     end
 end
 
-logpdf(d::Cosine, x::Real) = log(pdf(d, x))
+function logpdf(d::Cosine{T}, x::S) where {T<:Real, S<:Real}
+    if insupport(d, x)
+        z = (x - d.μ) / d.σ
+        return log1p(cospi(z)) - log(2d.σ)
+    else
+        return typemin(promote_type(T, S))
+    end
+end
 
 function cdf(d::Cosine{T}, x::S) where {T<:Real, S<:Real}
     W = promote_type(T, S)
-    if x < d.μ - d.σ
-        return zero(W)
-    end
-    if x > d.μ + d.σ
-        return one(W)
-    end
+
+    x < d.μ - d.σ && return zero(W)
+    x > d.μ + d.σ && return one(W)
+
     z = (x - d.μ) / d.σ
     (1 + z + sinpi(z) * invπ) / 2
 end
 
-function cdf(d::Cosine{T}, x::S) where {T<:Real, S<:Real}
+function ccdf(d::Cosine{T}, x::S) where {T<:Real, S<:Real}
     W = promote_type(T, S)
-    if x < d.μ - d.σ
-        return one(W)
-    end
-    if x > d.μ + d.σ
-        return zero(W)
-    end
+
+    x < d.μ - d.σ && return one(W)
+    x > d.μ + d.σ && return zero(W)
+
     nz = (d.μ - x) / d.σ
     (1 + nz + sinpi(nz) * invπ) / 2
 end
 
 quantile(d::Cosine, p::Real) = quantile_bisect(d, p)
 
-import IrrationalConstants: invπ
-import LogExpFunctions: logabssinh, log1psq
-
 function mgf(d::Cosine, t::Real)
     σt, μt = d.σ * t, d.μ*t
     z = iszero(σt) ? one(float(σt)) : sinh(σt)/σt

From 2f37977c14846b6a209f8cafe5f27e5012c8d08f Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jakub=20=C5=9Al=C4=99zak?=
 <128084860+jaksle@users.noreply.github.com>
Date: Fri, 5 Dec 2025 01:16:10 +0100
Subject: [PATCH 14/15] Update cosine.jl

---
 test/univariate/continuous/cosine.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/test/univariate/continuous/cosine.jl b/test/univariate/continuous/cosine.jl
index db4496fe19..e05b86da6d 100644
--- a/test/univariate/continuous/cosine.jl
+++ b/test/univariate/continuous/cosine.jl
@@ -5,7 +5,7 @@
         @test cgf(Cosine(-1, 2), 2) ≈ -2 + log(sinh(4)) - log(4) - log(1 + 16π^-2)
     end
 
-    @testset "affine transfomations" begin
+    @testset "affine transformations" begin
         @test -Cosine(1, 1) == Cosine(-1, 1)
         @test 3Cosine(1, 2) == Cosine(3, 6)
         @test Cosine(0, 2) + 42 == Cosine(42, 2)

From f3d5850bca3fe70e39a71bdbcebce0332aff3b95 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jakub=20=C5=9Al=C4=99zak?=
 <128084860+jaksle@users.noreply.github.com>
Date: Fri, 5 Dec 2025 23:35:31 +0100
Subject: [PATCH 15/15] add invpi to cf

---
 src/univariate/continuous/cosine.jl | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/src/univariate/continuous/cosine.jl b/src/univariate/continuous/cosine.jl
index e2d4b712f7..33a6527e7a 100644
--- a/src/univariate/continuous/cosine.jl
+++ b/src/univariate/continuous/cosine.jl
@@ -100,22 +100,22 @@ end
 quantile(d::Cosine, p::Real) = quantile_bisect(d, p)
 
 function mgf(d::Cosine, t::Real)
-    σt, μt = d.σ * t, d.μ*t
+    σt, μt = d.σ * t, d.μ * t
     z = iszero(σt) ? one(float(σt)) : sinh(σt)/σt
     return exp(μt) * (z / (1 + (invπ * σt)^2))
 end
 
 function cgf(d::Cosine, t::Real)
-    σt, μt = d.σ * t, d.μ*t
+    σt, μt = d.σ * t, d.μ * t
     z = iszero(σt) ? zero(float(σt)) : logabssinh(σt) - log(σt)
     return μt + z - log1psq(invπ * σt)
 end
 
 function cf(d::Cosine, t::Real)
-    σt, μt = d.σ * t, d.μ*t
+    σt, μt = d.σ * t, d.μ * t
     abs(σt) ≈ π && return cis(μt) / 2
     z = iszero(σt) ? one(float(σt)) : sin(σt)/σt
-    return π^2 * cis(μt) * z / (π^2 - (σt)^2)
+    return cis(μt) * z / (1 - (invπ * σt)^2)
 end
 
 #### Affine transformations