diff --git a/README.md b/README.md
index 11dafa8f0..1182d7898 100644
--- a/README.md
+++ b/README.md
@@ -1471,6 +1471,7 @@ $probabilities = ['a' => 0.3, 'b' => 0.2, 'c' => 0.5]; // probabilities for cate
 $categorical   = new Discrete\Categorical($k, $probabilities);
 $pmf_a         = $categorical->pmf('a');
 $mode          = $categorical->mode();
+$random        = $categorical->rand(); // returns 'a' or 'b' or 'c'
 
 // Geometric distribution (failures before the first success)
 $p         = 0.5; // success probability
@@ -1549,6 +1550,7 @@ $cdf     = $uniform->cdf($k);
 $μ       = $uniform->mean();
 $median  = $uniform->median();
 $σ²      = $uniform->variance();
+$random  = $uniform->rand();
 
 // Zipf distribution
 $k    = 2;   // rank
diff --git a/src/Probability/Distribution/Discrete/Categorical.php b/src/Probability/Distribution/Discrete/Categorical.php
index 4c2c2cf2d..a3b1ce8de 100644
--- a/src/Probability/Distribution/Discrete/Categorical.php
+++ b/src/Probability/Distribution/Discrete/Categorical.php
@@ -27,6 +27,14 @@ class Categorical extends Discrete
      */
     private $probabilities;
 
+    /**
+     * @var array<int|string, int|float>|null
+     * Cached CDF when pmf sorted from most probable category
+     * to least probable category.
+     * This is only useful for repeated sampling using Categorical::rand()
+     */
+    private $sorted_cdf = null;
+
     /**
      * Distribution constructor
      *
@@ -123,4 +131,45 @@ public function __get(string $name)
                 throw new Exception\BadDataException("$name is not a valid gettable parameter");
         }
     }
+
+    /**
+     * Sample a random category and return its key
+     *
+     * @return int|string
+     */
+    public function rand()
+    {
+        // calculate sorted cdf or use cached array
+        if (is_null($this->sorted_cdf)) {
+            // sort probabilities in descending order
+            $sorted_probabilities = $this->probabilities; // copy as arsort works in place
+            arsort($sorted_probabilities, SORT_NUMERIC);
+
+            // calculate cdf
+            $cdf = [];
+            $sum = 0.0;
+            foreach ($sorted_probabilities as $category => $pᵢ) {
+                $sum += $pᵢ;
+                $cdf[$category] = $sum;
+            }
+
+            $this->sorted_cdf = $cdf;
+        }
+
+        $rand = \random_int(0, \PHP_INT_MAX) / \PHP_INT_MAX; // [0, 1]
+
+        // find first element in sorted cdf that is larger than $rand
+        // for large arrays, performance could be improved by using binary search instead
+        // also possible with array_find_key in PHP >=8.4
+        foreach ($this->sorted_cdf as $category => $v) {
+            if ($v >= $rand) {
+                return $category;
+            }
+        }
+
+        // should only end up here if due to rounding errors the sum of probabilities
+        // is less than 1.0 and the generated random value is larger than the sum
+        // should be very unlikely, but possible
+        return array_key_last($this->sorted_cdf);
+    }
 }
diff --git a/src/Probability/Distribution/Discrete/Uniform.php b/src/Probability/Distribution/Discrete/Uniform.php
index f1eabf71d..86cebbf8e 100644
--- a/src/Probability/Distribution/Discrete/Uniform.php
+++ b/src/Probability/Distribution/Discrete/Uniform.php
@@ -154,4 +154,14 @@ public function variance(): float
 
         return (($b - $a + 1) ** 2 - 1) / 12;
     }
+
+    /**
+     * Random number sampled from the distribution
+     *
+     * @return int
+     */
+    public function rand(): int
+    {
+        return \random_int($this->a, $this->b);
+    }
 }
diff --git a/tests/Probability/Distribution/Discrete/CategoricalTest.php b/tests/Probability/Distribution/Discrete/CategoricalTest.php
index a54d48583..0983ce2ac 100644
--- a/tests/Probability/Distribution/Discrete/CategoricalTest.php
+++ b/tests/Probability/Distribution/Discrete/CategoricalTest.php
@@ -237,4 +237,39 @@ public function testGetException()
         // When
         $does_not_exist = $categorical->does_not_exist;
     }
+
+
+    /**
+     * @test rand
+     */
+    public function testRand()
+    {
+        // Given
+        $k             = 3;
+        $probabilities = ['a' => 0.2, 'b' => 0.5, 'c' => 0.3];
+        $categorical   = new Categorical($k, $probabilities);
+
+        // When
+        $rand = $categorical->rand();
+
+        // Then
+        $this->assertContains($rand, ['a', 'b', 'c']);
+    }
+
+    /**
+     * @test rand with certainty
+     */
+    public function testRandCertain()
+    {
+        // Given
+        $k             = 3;
+        $probabilities = ['a' => 0.0, 'b' => 1.0, 'c' => 0.0];
+        $categorical   = new Categorical($k, $probabilities);
+
+        // When
+        $rand = $categorical->rand();
+
+        // Then
+        $this->assertEquals('b', $rand);
+    }
 }
diff --git a/tests/Probability/Distribution/Discrete/UniformTest.php b/tests/Probability/Distribution/Discrete/UniformTest.php
index ffafbdaa5..b881865ee 100644
--- a/tests/Probability/Distribution/Discrete/UniformTest.php
+++ b/tests/Probability/Distribution/Discrete/UniformTest.php
@@ -175,4 +175,23 @@ public function dataProviderForVariance(): array
             [2, 4, 0.66666666666667],
         ];
     }
+
+    /**
+     * @test rand
+     */
+    public function testRand()
+    {
+        // Given
+        $a = 10;
+        $b = 11;
+        $uniform = new Uniform($a, $b);
+
+        // When
+        $random = $uniform->rand();
+
+        // Then
+        $this->assertTrue(\is_numeric($random));
+        $this->assertTrue($a <= $random);
+        $this->assertTrue($random <= $b);
+    }
 }