diff --git a/rand_distr/src/poisson.rs b/rand_distr/src/poisson.rs
index 28f835ab7b8..436131f34c9 100644
--- a/rand_distr/src/poisson.rs
+++ b/rand_distr/src/poisson.rs
@@ -138,7 +138,7 @@ where Standard: Distribution<N>
 }
 
 impl<N: Float> Distribution<u64> for Poisson<N>
-where Standard: Distribution<N>
+    where Standard: Distribution<N>
 {
     #[inline]
     fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> u64 {
@@ -147,10 +147,27 @@ where Standard: Distribution<N>
     }
 }
 
+impl<N: Float> Distribution<usize> for Poisson<N>
+    where Standard: Distribution<N>
+{
+    #[inline]
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> usize {
+        let result: N = self.sample(rng);
+        result.to_usize().unwrap()
+    }
+}
+
 #[cfg(test)]
 mod test {
     use super::*;
 
+    #[test]
+    fn poisson_usize() {
+        let poisson = Poisson::new(10.0).unwrap();
+        let mut rng = crate::test::rng(123);
+        let s_usize: usize = poisson.sample(&mut rng);
+    }
+
     #[test]
     fn test_poisson_10() {
         let poisson = Poisson::new(10.0).unwrap();
diff --git a/rand_distr/src/utils.rs b/rand_distr/src/utils.rs
index 478aacf7625..bf79e06149a 100644
--- a/rand_distr/src/utils.rs
+++ b/rand_distr/src/utils.rs
@@ -42,6 +42,9 @@ pub trait Float:
     /// Support converting to an unsigned integer.
     fn to_u64(self) -> Option<u64>;
 
+    /// Support converting to an unsigned integer.
+    fn to_usize(self) -> Option<usize>;
+
     /// Take the absolute value of self
     fn abs(self) -> Self;
     /// Take the largest integer less than or equal to self
@@ -82,6 +85,15 @@ impl Float for f32 {
         }
     }
 
+    #[inline]
+    fn to_usize(self) -> Option<usize> {
+        if self >= 0. && self <= ::core::usize::MAX as f32 {
+            Some(self as usize)
+        } else {
+            None
+        }
+    }
+
     #[inline]
     fn abs(self) -> Self {
         self.abs()
@@ -145,6 +157,14 @@ impl Float for f64 {
             None
         }
     }
+    #[inline]
+    fn to_usize(self) -> Option<usize> {
+        if self >= 0. && self <= ::core::usize::MAX as f64 {
+            Some(self as usize)
+        } else {
+            None
+        }
+    }
 
     #[inline]
     fn abs(self) -> Self {