diff --git a/Manifest.toml b/Manifest.toml
new file mode 100644
index 0000000000..24c24f39c5
--- /dev/null
+++ b/Manifest.toml
@@ -0,0 +1,283 @@
+# This file is machine-generated - editing it directly is not advised
+
+julia_version = "1.11.7"
+manifest_format = "2.0"
+project_hash = "962aad218adea1a5fe37ec65f3ff696c6a646b6b"
+
+[[deps.AliasTables]]
+deps = ["PtrArrays", "Random"]
+git-tree-sha1 = "9876e1e164b144ca45e9e3198d0b689cadfed9ff"
+uuid = "66dad0bd-aa9a-41b7-9441-69ab47430ed8"
+version = "1.1.3"
+
+[[deps.Artifacts]]
+uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
+version = "1.11.0"
+
+[[deps.Combinatorics]]
+git-tree-sha1 = "c761b00e7755700f9cdf5b02039939d1359330e1"
+uuid = "861a8166-3701-5b0c-9a16-15d98fcdc6aa"
+version = "1.1.0"
+
+[[deps.CompilerSupportLibraries_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
+version = "1.1.1+0"
+
+[[deps.DataAPI]]
+git-tree-sha1 = "abe83f3a2f1b857aac70ef8b269080af17764bbe"
+uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
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+
+[[deps.DataStructures]]
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+
+[[deps.Dates]]
+deps = ["Printf"]
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+version = "1.11.0"
+
+[[deps.DocStringExtensions]]
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+uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
+version = "0.9.5"
+
+[[deps.FillArrays]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "2f979084d1e13948a3352cf64a25df6bd3b4dca3"
+uuid = "1a297f60-69ca-5386-bcde-b61e274b549b"
+version = "1.16.0"
+
+    [deps.FillArrays.extensions]
+    FillArraysPDMatsExt = "PDMats"
+    FillArraysSparseArraysExt = "SparseArrays"
+    FillArraysStaticArraysExt = "StaticArrays"
+    FillArraysStatisticsExt = "Statistics"
+
+    [deps.FillArrays.weakdeps]
+    PDMats = "90014a1f-27ba-587c-ab20-58faa44d9150"
+    SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+    StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
+    Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
+
+[[deps.HypergeometricFunctions]]
+deps = ["LinearAlgebra", "OpenLibm_jll", "SpecialFunctions"]
+git-tree-sha1 = "68c173f4f449de5b438ee67ed0c9c748dc31a2ec"
+uuid = "34004b35-14d8-5ef3-9330-4cdb6864b03a"
+version = "0.3.28"
+
+[[deps.IrrationalConstants]]
+git-tree-sha1 = "b2d91fe939cae05960e760110b328288867b5758"
+uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
+version = "0.2.6"
+
+[[deps.JLLWrappers]]
+deps = ["Artifacts", "Preferences"]
+git-tree-sha1 = "0533e564aae234aff59ab625543145446d8b6ec2"
+uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
+version = "1.7.1"
+
+[[deps.Libdl]]
+uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
+version = "1.11.0"
+
+[[deps.LinearAlgebra]]
+deps = ["Libdl", "OpenBLAS_jll", "libblastrampoline_jll"]
+uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+version = "1.11.0"
+
+[[deps.LogExpFunctions]]
+deps = ["DocStringExtensions", "IrrationalConstants", "LinearAlgebra"]
+git-tree-sha1 = "13ca9e2586b89836fd20cccf56e57e2b9ae7f38f"
+uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
+version = "0.3.29"
+
+    [deps.LogExpFunctions.extensions]
+    LogExpFunctionsChainRulesCoreExt = "ChainRulesCore"
+    LogExpFunctionsChangesOfVariablesExt = "ChangesOfVariables"
+    LogExpFunctionsInverseFunctionsExt = "InverseFunctions"
+
+    [deps.LogExpFunctions.weakdeps]
+    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+    ChangesOfVariables = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0"
+    InverseFunctions = "3587e190-3f89-42d0-90ee-14403ec27112"
+
+[[deps.Missings]]
+deps = ["DataAPI"]
+git-tree-sha1 = "ec4f7fbeab05d7747bdf98eb74d130a2a2ed298d"
+uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
+version = "1.2.0"
+
+[[deps.OpenBLAS_jll]]
+deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
+uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"
+version = "0.3.27+1"
+
+[[deps.OpenLibm_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "05823500-19ac-5b8b-9628-191a04bc5112"
+version = "0.8.5+0"
+
+[[deps.OpenSpecFun_jll]]
+deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "1346c9208249809840c91b26703912dff463d335"
+uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
+version = "0.5.6+0"
+
+[[deps.OrderedCollections]]
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+uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
+version = "1.8.1"
+
+[[deps.PDMats]]
+deps = ["LinearAlgebra", "SparseArrays", "SuiteSparse"]
+git-tree-sha1 = "e4cff168707d441cd6bf3ff7e4832bdf34278e4a"
+uuid = "90014a1f-27ba-587c-ab20-58faa44d9150"
+version = "0.11.37"
+weakdeps = ["StatsBase"]
+
+    [deps.PDMats.extensions]
+    StatsBaseExt = "StatsBase"
+
+[[deps.Preferences]]
+deps = ["TOML"]
+git-tree-sha1 = "8b770b60760d4451834fe79dd483e318eee709c4"
+uuid = "21216c6a-2e73-6563-6e65-726566657250"
+version = "1.5.2"
+
+[[deps.Printf]]
+deps = ["Unicode"]
+uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
+version = "1.11.0"
+
+[[deps.PtrArrays]]
+git-tree-sha1 = "4fbbafbc6251b883f4d2705356f3641f3652a7fe"
+uuid = "43287f4e-b6f4-7ad1-bb20-aadabca52c3d"
+version = "1.4.0"
+
+[[deps.QuadGK]]
+deps = ["DataStructures", "LinearAlgebra"]
+git-tree-sha1 = "5e8e8b0ab68215d7a2b14b9921a946fee794749e"
+uuid = "1fd47b50-473d-5c70-9696-f719f8f3bcdc"
+version = "2.11.3"
+
+    [deps.QuadGK.extensions]
+    QuadGKEnzymeExt = "Enzyme"
+
+    [deps.QuadGK.weakdeps]
+    Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
+
+[[deps.Random]]
+deps = ["SHA"]
+uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+version = "1.11.0"
+
+[[deps.Reexport]]
+git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
+uuid = "189a3867-3050-52da-a836-e630ba90ab69"
+version = "1.2.2"
+
+[[deps.Rmath]]
+deps = ["Random", "Rmath_jll"]
+git-tree-sha1 = "5b3d50eb374cea306873b371d3f8d3915a018f0b"
+uuid = "79098fc4-a85e-5d69-aa6a-4863f24498fa"
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+
+[[deps.Rmath_jll]]
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+[[deps.SHA]]
+uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
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+
+[[deps.Serialization]]
+uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
+version = "1.11.0"
+
+[[deps.SortingAlgorithms]]
+deps = ["DataStructures"]
+git-tree-sha1 = "64d974c2e6fdf07f8155b5b2ca2ffa9069b608d9"
+uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
+version = "1.2.2"
+
+[[deps.SparseArrays]]
+deps = ["Libdl", "LinearAlgebra", "Random", "Serialization", "SuiteSparse_jll"]
+uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+version = "1.11.0"
+
+[[deps.SpecialFunctions]]
+deps = ["IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
+git-tree-sha1 = "2700b235561b0335d5bef7097a111dc513b8655e"
+uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
+version = "2.7.2"
+
+    [deps.SpecialFunctions.extensions]
+    SpecialFunctionsChainRulesCoreExt = "ChainRulesCore"
+
+    [deps.SpecialFunctions.weakdeps]
+    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+
+[[deps.Statistics]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "ae3bb1eb3bba077cd276bc5cfc337cc65c3075c0"
+uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
+version = "1.11.1"
+weakdeps = ["SparseArrays"]
+
+    [deps.Statistics.extensions]
+    SparseArraysExt = ["SparseArrays"]
+
+[[deps.StatsAPI]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "178ed29fd5b2a2cfc3bd31c13375ae925623ff36"
+uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
+version = "1.8.0"
+
+[[deps.StatsBase]]
+deps = ["AliasTables", "DataAPI", "DataStructures", "IrrationalConstants", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
+git-tree-sha1 = "aceda6f4e598d331548e04cc6b2124a6148138e3"
+uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
+version = "0.34.10"
+
+[[deps.StatsFuns]]
+deps = ["HypergeometricFunctions", "IrrationalConstants", "LogExpFunctions", "Reexport", "Rmath", "SpecialFunctions"]
+git-tree-sha1 = "91f091a8716a6bb38417a6e6f274602a19aaa685"
+uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
+version = "1.5.2"
+
+    [deps.StatsFuns.extensions]
+    StatsFunsChainRulesCoreExt = "ChainRulesCore"
+    StatsFunsInverseFunctionsExt = "InverseFunctions"
+
+    [deps.StatsFuns.weakdeps]
+    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+    InverseFunctions = "3587e190-3f89-42d0-90ee-14403ec27112"
+
+[[deps.SuiteSparse]]
+deps = ["Libdl", "LinearAlgebra", "Serialization", "SparseArrays"]
+uuid = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9"
+
+[[deps.SuiteSparse_jll]]
+deps = ["Artifacts", "Libdl", "libblastrampoline_jll"]
+uuid = "bea87d4a-7f5b-5778-9afe-8cc45184846c"
+version = "7.7.0+0"
+
+[[deps.TOML]]
+deps = ["Dates"]
+uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
+version = "1.0.3"
+
+[[deps.Unicode]]
+uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
+version = "1.11.0"
+
+[[deps.libblastrampoline_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
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diff --git a/Project.toml b/Project.toml
index 36efe12703..1e54eca942 100644
--- a/Project.toml
+++ b/Project.toml
@@ -6,6 +6,7 @@ version = "0.25.125"
 [deps]
 AliasTables = "66dad0bd-aa9a-41b7-9441-69ab47430ed8"
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+Combinatorics = "861a8166-3701-5b0c-9a16-15d98fcdc6aa"
 DensityInterface = "b429d917-457f-4dbc-8f4c-0cc954292b1d"
 FillArrays = "1a297f60-69ca-5386-bcde-b61e274b549b"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
@@ -36,6 +37,7 @@ Aqua = "0.8.9"
 Calculus = "0.5"
 ChainRulesCore = "1"
 ChainRulesTestUtils = "1"
+Combinatorics = "1.1.0"
 DensityInterface = "0.4"
 Distributed = "<0.0.1, 1"
 FillArrays = "0.9, 0.10, 0.11, 0.12, 0.13, 1"
diff --git a/src/multivariate/multinomial.jl b/src/multivariate/multinomial.jl
index f365450cab..57997f97ca 100644
--- a/src/multivariate/multinomial.jl
+++ b/src/multivariate/multinomial.jl
@@ -1,3 +1,5 @@
+using Combinatorics
+
 """
 The [Multinomial distribution](http://en.wikipedia.org/wiki/Multinomial_distribution)
 generalizes the *binomial distribution*. Consider n independent draws from a Categorical
@@ -19,6 +21,7 @@ Multinomial(n, k)   # Multinomial distribution for n trials with equal probabili
                     # over 1:k
 ```
 """
+
 struct Multinomial{T<:Real, TV<:AbstractVector{T}} <: DiscreteMultivariateDistribution
     n::Int
     p::TV
@@ -162,6 +165,53 @@ function _logpdf(d::Multinomial, x::AbstractVector{T}) where T<:Real
     return s
 end
 
+"""
+    cdf(d::Multinomial, x::AbstractVector{<:Real})
+
+Compute the cumulative distribution function (CDF) of the Multinomial distribution `d` evaluated at `x`. 
+
+This calculates the probability of observing counts less than or equal to the corresponding 
+values in `x` for all categories simultaneously.
+"""
+function cdf(d::Multinomial, x::AbstractVector{<:Real})
+    n = d.n
+    k = length(d.p)
+    
+    any(x .< 0) && return 0.0
+    
+    sum(x) < n && return 0.0
+
+    pool = Int[]
+    for i in 1:k
+        max_capacity = min(floor(Int, x[i]), n)
+        append!(pool, fill(i, max_capacity))
+    end
+
+    total_prob = 0.0
+    
+    y = zeros(Int, k)
+
+    for combo in multiset_combinations(pool, n)
+        fill!(y, 0)
+        for category in combo
+            y[category] += 1
+        end
+    
+        total_prob += pdf(d, y)
+    end
+    
+    return total_prob
+end
+
+"""
+    logcdf(d::Multinomial, x::AbstractVector{<:Real})
+
+Compute the log of the cumulative distribution function of the Multinomial distribution `d` evaluated at `x`.
+"""
+function logcdf(d::Multinomial, x::AbstractVector{<:Real})
+    return log(cdf(d, x))
+end
+
 # Sampling
 
 # if only a single sample is requested, no alias table is created