diff --git a/src/sampling.jl b/src/sampling.jl
index 609c7d48..4551476a 100644
--- a/src/sampling.jl
+++ b/src/sampling.jl
@@ -591,7 +591,9 @@ Optionally specify a random number generator `rng` as the first argument
 function sample(rng::AbstractRNG, wv::AbstractWeights)
     1 == firstindex(wv) ||
         throw(ArgumentError("non 1-based arrays are not supported"))
-    t = rand(rng) * sum(wv)
+    wsum = sum(wv)
+    isfinite(wsum) || throw(ArgumentError("only finite weights are supported"))
+    t = rand(rng) * wsum
     n = length(wv)
     i = 1
     cw = wv[1]
@@ -654,6 +656,7 @@ function alias_sample!(rng::AbstractRNG, a::AbstractArray, wv::AbstractWeights,
         throw(ArgumentError("output array x must not share memory with input array a"))
     1 == firstindex(a) == firstindex(wv) ||
         throw(ArgumentError("non 1-based arrays are not supported"))
+    isfinite(sum(wv)) || throw(ArgumentError("only finite weights are supported"))
     length(wv) == length(a) || throw(DimensionMismatch("Inconsistent lengths."))
 
     # create alias table
@@ -688,13 +691,14 @@ function naive_wsample_norep!(rng::AbstractRNG, a::AbstractArray,
         throw(ArgumentError("output array x must not share memory with weights array wv"))
     1 == firstindex(a) == firstindex(wv) == firstindex(x) ||
         throw(ArgumentError("non 1-based arrays are not supported"))
+    wsum = sum(wv)
+    isfinite(wsum) || throw(ArgumentError("only finite weights are supported"))
     n = length(a)
     length(wv) == n || throw(DimensionMismatch("Inconsistent lengths."))
     k = length(x)
 
     w = Vector{Float64}(undef, n)
     copyto!(w, wv)
-    wsum = sum(wv)
 
     for i = 1:k
         u = rand(rng) * wsum
@@ -734,6 +738,7 @@ function efraimidis_a_wsample_norep!(rng::AbstractRNG, a::AbstractArray,
         throw(ArgumentError("output array x must not share memory with weights array wv"))
     1 == firstindex(a) == firstindex(wv) == firstindex(x) ||
         throw(ArgumentError("non 1-based arrays are not supported"))
+    isfinite(sum(wv)) || throw(ArgumentError("only finite weights are supported"))
     n = length(a)
     length(wv) == n || throw(DimensionMismatch("a and wv must be of same length (got $n and $(length(wv)))."))
     k = length(x)
@@ -775,6 +780,7 @@ function efraimidis_ares_wsample_norep!(rng::AbstractRNG, a::AbstractArray,
         throw(ArgumentError("output array x must not share memory with weights array wv"))
     1 == firstindex(a) == firstindex(wv) == firstindex(x) ||
         throw(ArgumentError("non 1-based arrays are not supported"))
+    isfinite(sum(wv)) || throw(ArgumentError("only finite weights are supported"))
     n = length(a)
     length(wv) == n || throw(DimensionMismatch("a and wv must be of same length (got $n and $(length(wv)))."))
     k = length(x)
@@ -848,6 +854,7 @@ function efraimidis_aexpj_wsample_norep!(rng::AbstractRNG, a::AbstractArray,
         throw(ArgumentError("output array x must not share memory with weights array wv"))
     1 == firstindex(a) == firstindex(wv) == firstindex(x) ||
         throw(ArgumentError("non 1-based arrays are not supported"))
+    isfinite(sum(wv)) || throw(ArgumentError("only finite weights are supported"))
     n = length(a)
     length(wv) == n || throw(DimensionMismatch("a and wv must be of same length (got $n and $(length(wv)))."))
     k = length(x)
diff --git a/src/scalarstats.jl b/src/scalarstats.jl
index 1671bd01..2936f927 100644
--- a/src/scalarstats.jl
+++ b/src/scalarstats.jl
@@ -163,6 +163,7 @@ end
 # Weighted mode of arbitrary vectors of values
 function mode(a::AbstractVector, wv::AbstractWeights{T}) where T <: Real
     isempty(a) && throw(ArgumentError("mode is not defined for empty collections"))
+    isfinite(sum(wv)) || throw(ArgumentError("only finite weights are supported"))
     length(a) == length(wv) ||
         throw(ArgumentError("data and weight vectors must be the same size, got $(length(a)) and $(length(wv))"))
 
@@ -184,6 +185,7 @@ end
 
 function modes(a::AbstractVector, wv::AbstractWeights{T}) where T <: Real
     isempty(a) && throw(ArgumentError("mode is not defined for empty collections"))
+    isfinite(sum(wv)) || throw(ArgumentError("only finite weights are supported"))
     length(a) == length(wv) ||
         throw(ArgumentError("data and weight vectors must be the same size, got $(length(a)) and $(length(wv))"))
 
diff --git a/src/weights.jl b/src/weights.jl
index f5f51510..ec415d3d 100644
--- a/src/weights.jl
+++ b/src/weights.jl
@@ -716,6 +716,7 @@ function quantile(v::AbstractVector{<:Real}{V}, w::AbstractWeights{W}, p::Abstra
     # checks
     isempty(v) && throw(ArgumentError("quantile of an empty array is undefined"))
     isempty(p) && throw(ArgumentError("empty quantile array"))
+    isfinite(sum(w)) || throw(ArgumentError("only finite weights are supported"))
     all(x -> 0 <= x <= 1, p) || throw(ArgumentError("input probability out of [0,1] range"))
 
     w.sum == 0 && throw(ArgumentError("weight vector cannot sum to zero"))
diff --git a/test/weights.jl b/test/weights.jl
index 2180c88a..76277e02 100644
--- a/test/weights.jl
+++ b/test/weights.jl
@@ -1,6 +1,15 @@
 using StatsBase
 using LinearAlgebra, Random, SparseArrays, Test
 
+
+# minimal custom weights type for tests below
+struct MyWeights <: AbstractWeights{Float64, Float64, Vector{Float64}}
+    values::Vector{Float64}
+    sum::Float64
+end
+MyWeights(values) = MyWeights(values, sum(values))
+
+
 @testset "StatsBase.Weights" begin
 weight_funcs = (weights, aweights, fweights, pweights)
 
@@ -610,4 +619,11 @@ end
     end
 end
 
+@testset "custom weight types" begin
+    @test mean([1, 2, 3], MyWeights([1, 4, 10])) ≈ 2.6
+    @test mean([1, 2, 3], MyWeights([NaN, 4, 10])) |> isnan
+    @test mode([1, 2, 3], MyWeights([1, 4, 10])) == 3
+    @test_throws ArgumentError mode([1, 2, 3], MyWeights([NaN, 4, 10]))
+end
+
 end # @testset StatsBase.Weights