diff --git a/core/src/main/scala/dimwit/stats/IndependentDistributions.scala b/core/src/main/scala/dimwit/stats/IndependentDistributions.scala
index 975ed4a7..39d1b558 100644
--- a/core/src/main/scala/dimwit/stats/IndependentDistributions.scala
+++ b/core/src/main/scala/dimwit/stats/IndependentDistributions.scala
@@ -175,3 +175,29 @@ object Beta:
   def apply[T <: Tuple: Labels, V: IsFloating](alpha: Tensor[T, V], beta: Tensor[T, V]): Beta[T, V] =
     require(alpha.shape.dimensions == beta.shape.dimensions, "alpha and beta must have the same dimensions")
     new Beta(alpha, beta)
+
+/** Exponential distribution */
+class Exponential[T <: Tuple: Labels, V: IsFloating](val rate: Tensor[T, V]) extends IndependentDistribution[T, V]:
+
+  lazy val scale = (Tensor0(1f).asType(VType[V]) /! rate).jaxValue
+
+  override def elementWiseLogProb(x: Tensor[T, V]): Tensor[T, LogProb] =
+    liftPyTensor(jstats.expon.logpdf(x.jaxValue, scale = scale))
+
+  override def sample(k: Random.Key): Tensor[T, V] =
+    // samples from jrandom.exponential are always with scale=1,
+    // so we need to divide by the rate to get the correct distribution
+    val stndExp = liftPyTensor[T, V](
+      Jax.jrandom.exponential(k.jaxKey, shape = rate.shape.dimensions.toPythonProxy)
+    )
+    stndExp / rate
+
+class Poisson[T <: Tuple: Labels, V: IsInteger](val rate: Tensor[T, V]) extends IndependentDistribution[T, V]:
+
+  override def elementWiseLogProb(x: Tensor[T, V]): Tensor[T, LogProb] =
+    liftPyTensor(jstats.poisson.logpmf(x.jaxValue, mu = rate.jaxValue))
+
+  override def sample(k: Random.Key): Tensor[T, V] =
+    liftPyTensor(
+      Jax.jrandom.poisson(k.jaxKey, lam = rate.jaxValue, shape = rate.shape.dimensions.toPythonProxy)
+    )
diff --git a/core/src/test/scala/dimwit/stats/DistributionSuite.scala b/core/src/test/scala/dimwit/stats/DistributionSuite.scala
index 66095632..adb84026 100644
--- a/core/src/test/scala/dimwit/stats/DistributionSuite.scala
+++ b/core/src/test/scala/dimwit/stats/DistributionSuite.scala
@@ -335,3 +335,50 @@ class DistributionSuite extends DimwitTest:
       // Mean of Beta distribution is alpha / (alpha + beta)
       val expectedMeans = betaDist.alpha / (betaDist.alpha + betaDist.beta)
       sampleMeans should approxEqual(expectedMeans, 0.02f)
+
+  describe("Exponential"):
+    it("logProbs matches JAX"):
+      val rate = Tensor(Shape(Axis[A] -> 3)).fromArray(Array(0.5f, 1.0f, 2.0f))
+      val x = Tensor(Shape(Axis[A] -> 3)).fromArray(Array(0.5f, 1.0f, 0.3f))
+
+      val dist = Exponential(rate)
+      val scalaLogProbs = dist.elementWiseLogProb(x)
+      val scale = Tensor(Shape(Axis[A] -> 3)).fromArray(Array(2.0f, 1.0f, 0.5f))
+      val jaxLogProbs = liftPyTensor1(Axis[A], VType[Float32])(
+        jstats.expon.logpdf(x.jaxValue, scale = scale.jaxValue)
+      )
+      scalaLogProbs.asFloat should approxEqual(jaxLogProbs)
+
+    it("sample means approximates 1/rate"):
+      val exponential = Exponential(
+        Tensor(Shape(Axis[A] -> 2)).fromArray(Array(0.5f, 2.0f))
+      )
+      val key = Random.Key(42)
+      val samples = key.splitvmap(Axis[Samples] -> 10000)(k => exponential.sample(k))
+      val sampleMeans = samples.mean(Axis[Samples])
+      // Mean of Exponential(rate) is 1/rate
+      val expectedMeans = Tensor(Shape(Axis[A] -> 2)).fromArray(Array(2.0f, 0.5f))
+      sampleMeans should approxEqual(expectedMeans, 0.1f)
+
+  describe("Poisson"):
+    it("logProbs matches JAX"):
+      val rate = Tensor(Shape(Axis[A] -> 3)).fromArray(Array(1, 3, 10))
+      val x = Tensor(Shape(Axis[A] -> 3)).fromArray(Array(1, 2, 8))
+
+      val dist = Poisson(rate)
+      val scalaLogProbs = dist.elementWiseLogProb(x)
+      val jaxLogProbs = liftPyTensor1(Axis[A], VType[Float32])(
+        jstats.poisson.logpmf(x.jaxValue, mu = rate.jaxValue)
+      )
+      scalaLogProbs.asFloat should approxEqual(jaxLogProbs)
+
+    it("sample means approximates rate"):
+      val poisson = Poisson(
+        Tensor(Shape(Axis[A] -> 2)).fromArray(Array(1, 5))
+      )
+      val key = Random.Key(42)
+      val samples = key.splitvmap(Axis[Samples] -> 10000)(k => poisson.sample(k))
+      val sampleMeans = samples.asFloat32.mean(Axis[Samples])
+      // Mean of Poisson(lambda) is lambda
+      val expectedMeans = poisson.rate.asFloat32
+      sampleMeans should approxEqual(expectedMeans, 0.2f)