Add survival and log-survival function to distrax.Distribution base…

… class.

Note that by default we use a numerically not necessarily stable definition
of the survival function in terms of the CDF: sf(x) = 1-cdf(x) and similarly
for the log survival function.
More stable definitions should be implemented in future CLs for distributions,
for which they exist.

Added a test to `distribution.Uniform` where we will use the default behaviour.

PiperOrigin-RevId: 443160366

distrax/_src/distributions/distribution.py

@@ -188,6 +188,39 @@ def cdf(self, value: Array) -> Array:
     """
     return jnp.exp(self.log_cdf(value))
 
+  def survival_function(self, value: Array) -> Array:
+    """Evaluates the survival function at `value`.
+
+    Args:
+      value: An event.
+
+    Returns:
+      The survival function evaluated at `value`, i.e. P[X > value]
+    """
+    if not self.event_shape:
+      # Defined for univariate distributions only.
+      return 1. - self.cdf(value)
+    else:
+      raise NotImplementedError('`survival_function` is not defined for '
+                                f'distribution {self.name}')
+
+  def log_survival_function(self, value: Array) -> Array:
+    """Evaluates the log of the survival function at `value`.
+
+    Args:
+      value: An event.
+
+    Returns:
+      The log of the survival function evaluated at `value`, i.e.
+      log P[X > value]
+    """
+    if not self.event_shape:
+      # Defined for univariate distributions only.
+      return jnp.log1p(-self.cdf(value))
+    else:
+      raise NotImplementedError('`log_survival_function` is not defined for '
+                                f'distribution {self.name}')
+
   def mean(self) -> Array:
     """Calculates the mean."""
     raise NotImplementedError(

distrax/_src/distributions/distribution_test.py

@@ -205,6 +205,12 @@ def test_to_batch_shape_index_raises(self, index):
       distribution.to_batch_shape_index(
           batch_shape=(2, 3, 4), index=index)
 
+  def test_multivariate_survival_function_raises(self):
+    mult_dist = DummyMultivariateDist(42)
+    with self.assertRaises(NotImplementedError):
+      mult_dist.survival_function(jnp.zeros(42))
+    with self.assertRaises(NotImplementedError):
+      mult_dist.log_survival_function(jnp.zeros(42))
 
 if __name__ == '__main__':
   absltest.main()

distrax/_src/distributions/uniform_test.py

@@ -89,6 +89,8 @@ def test_sample_and_log_prob(self, distr_params, sample_shape):
       ('log_prob', 'log_prob'),
       ('prob', 'prob'),
       ('cdf', 'cdf'),
+      ('survival_function', 'survival_function'),
+      ('log_survival_function', 'log_survival_function')
   )
   def test_method_with_inputs(self, function_string):
     inputs = 10. * np.random.normal(size=(100,))