diff --git a/Cargo.lock.MSRV b/Cargo.lock.MSRV
index d7585419..9faa9327 100644
--- a/Cargo.lock.MSRV
+++ b/Cargo.lock.MSRV
@@ -347,12 +347,12 @@ dependencies = [
 
 [[package]]
 name = "kdtree"
-version = "0.7.0"
+version = "0.8.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "0f0a0e9f770b65bac9aad00f97a67ab5c5319effed07f6da385da3c2115e47ba"
+checksum = "9cd666c2aae5dde60d2f9bfa4e1f8c17698fce13d599c0f9b76725641fec13d9"
 dependencies = [
  "num-traits",
- "thiserror 1.0.69",
+ "thiserror",
 ]
 
 [[package]]
@@ -718,7 +718,7 @@ dependencies = [
  "nalgebra",
  "num-traits",
  "rand",
- "thiserror 2.0.19",
+ "thiserror",
 ]
 
 [[package]]
@@ -743,33 +743,13 @@ dependencies = [
  "unicode-ident",
 ]
 
-[[package]]
-name = "thiserror"
-version = "1.0.69"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "b6aaf5339b578ea85b50e080feb250a3e8ae8cfcdff9a461c9ec2904bc923f52"
-dependencies = [
- "thiserror-impl 1.0.69",
-]
-
 [[package]]
 name = "thiserror"
 version = "2.0.19"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "09a43598840e33d5b0331f38c5e30d13bb11c11210a4b58f0d9b18a5a5eefcd9"
 dependencies = [
- "thiserror-impl 2.0.19",
-]
-
-[[package]]
-name = "thiserror-impl"
-version = "1.0.69"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "4fee6c4efc90059e10f81e6d42c60a18f76588c3d74cb83a0b242a2b6c7504c1"
-dependencies = [
- "proc-macro2",
- "quote",
- "syn 2.0.119",
+ "thiserror-impl",
 ]
 
 [[package]]
diff --git a/Cargo.toml b/Cargo.toml
index 120e3bfa..6e3fd32e 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -53,7 +53,7 @@ optional = true
 default-features = false
 
 [dependencies.kdtree]
-version = "0.7.0"
+version = "0.8.1"
 optional = true
 
 [dev-dependencies]
diff --git a/src/density/kde.rs b/src/density/kde.rs
index caa17720..3d561d24 100644
--- a/src/density/kde.rs
+++ b/src/density/kde.rs
@@ -1,7 +1,7 @@
 use kdtree::distance::squared_euclidean;
 
 use crate::{
-    density::{Container, DensityError, nearest_neighbors},
+    density::{Container, DensityError, nearest_neighbors, neighborhood_radius},
     function::kernel::{Gaussian, Kernel},
 };
 
@@ -30,7 +30,7 @@ where
     if neighbors.is_empty() {
         Err(DensityError::EmptyNeighborhood)
     } else {
-        let radius = neighbors.last().unwrap().sqrt(); // safe to unwrap here since `neighbors` is not empty
+        let radius = neighborhood_radius(&neighbors).unwrap();
         let d = x.length() as i32;
         Ok((1. / (n_samples * radius.powi(d)))
             * samples
diff --git a/src/density/knn.rs b/src/density/knn.rs
index 1f58637d..95d44dd4 100644
--- a/src/density/knn.rs
+++ b/src/density/knn.rs
@@ -1,6 +1,6 @@
 use super::Container;
 use crate::{
-    density::{DensityError, nearest_neighbors},
+    density::{DensityError, nearest_neighbors, neighborhood_radius},
     function::gamma::gamma,
 };
 use core::f64::consts::PI;
@@ -30,7 +30,7 @@ where
     if neighbors.is_empty() {
         Err(DensityError::EmptyNeighborhood)
     } else {
-        let radius = neighbors.last().unwrap().sqrt();
+        let radius = neighborhood_radius(&neighbors).unwrap();
         let d = x.length() as f64;
         Ok((k / n_samples) * (gamma(d / 2. + 1.) / (PI.powf(d / 2.) * radius.powf(d))))
     }
diff --git a/src/density/mod.rs b/src/density/mod.rs
index cfb51cbc..0e18eca9 100644
--- a/src/density/mod.rs
+++ b/src/density/mod.rs
@@ -79,6 +79,14 @@ impl_container!(
 );
 pub type NearestNeighbors = (Vec<f64>, f64);
 
+pub(crate) fn neighborhood_radius(neighbors: &[f64]) -> Option<f64> {
+    neighbors
+        .iter()
+        .copied()
+        .max_by(f64::total_cmp)
+        .map(f64::sqrt)
+}
+
 pub(crate) fn nearest_neighbors<S, X>(
     x: &X,
     samples: &S,
@@ -118,6 +126,11 @@ mod tests {
 
     use super::*;
 
+    #[test]
+    fn neighborhood_radius_uses_farthest_distance() {
+        assert_eq!(neighborhood_radius(&[4.0, 1.0, 9.0, 2.0]), Some(3.0));
+    }
+
     #[test]
     fn test_vec_container() {
         let v1 = vec![1.0, 2.0, 3.0];