diff --git a/src/distributions/weighted_index.rs b/src/distributions/weighted_index.rs
index a75d41eae0c..1dc003bdc0e 100644
--- a/src/distributions/weighted_index.rs
+++ b/src/distributions/weighted_index.rs
@@ -102,13 +102,15 @@ impl<X: SampleUniform + PartialOrd> WeightedIndex<X> {
         let mut total_weight: X = iter.next().ok_or(WeightedError::NoItem)?.borrow().clone();
 
         let zero = <X as Default>::default();
-        if total_weight < zero {
+        if !(total_weight >= zero) {
             return Err(WeightedError::InvalidWeight);
         }
 
         let mut weights = Vec::<X>::with_capacity(iter.size_hint().0);
         for w in iter {
-            if *w.borrow() < zero {
+            // Note that `!(w >= x)` is not equivalent to `w < x` for partially
+            // ordered types due to NaNs which are equal to nothing.
+            if !(w.borrow() >= &zero) {
                 return Err(WeightedError::InvalidWeight);
             }
             weights.push(total_weight.clone());
@@ -158,7 +160,7 @@ impl<X: SampleUniform + PartialOrd> WeightedIndex<X> {
                     return Err(WeightedError::InvalidWeight);
                 }
             }
-            if *w < zero {
+            if !(*w >= zero) {
                 return Err(WeightedError::InvalidWeight);
             }
             if i >= self.cumulative_weights.len() + 1 {
@@ -256,6 +258,30 @@ mod test {
         assert_eq!(de_weighted_index.total_weight, weighted_index.total_weight);
     }
 
+    #[test]
+    fn test_accepting_nan(){
+        assert_eq!(
+            WeightedIndex::new(&[core::f32::NAN, 0.5]).unwrap_err(),
+            WeightedError::InvalidWeight,
+        );
+        assert_eq!(
+            WeightedIndex::new(&[core::f32::NAN]).unwrap_err(),
+            WeightedError::InvalidWeight,
+        );
+        assert_eq!(
+            WeightedIndex::new(&[0.5, core::f32::NAN]).unwrap_err(),
+            WeightedError::InvalidWeight,
+        );
+
+        assert_eq!(
+            WeightedIndex::new(&[0.5, 7.0])
+                .unwrap()
+                .update_weights(&[(0, &core::f32::NAN)])
+                .unwrap_err(),
+            WeightedError::InvalidWeight,
+        )
+    }
+
 
     #[test]
     #[cfg_attr(miri, ignore)] // Miri is too slow
@@ -399,8 +425,8 @@ pub enum WeightedError {
     /// The provided weight collection contains no items.
     NoItem,
 
-    /// A weight is either less than zero, greater than the supported maximum or
-    /// otherwise invalid.
+    /// A weight is either less than zero, greater than the supported maximum,
+    /// NaN, or otherwise invalid.
     InvalidWeight,
 
     /// All items in the provided weight collection are zero.