diff --git a/src/pyhf/infer/calculators.py b/src/pyhf/infer/calculators.py
index ed9642e085..18c8d078a7 100644
--- a/src/pyhf/infer/calculators.py
+++ b/src/pyhf/infer/calculators.py
@@ -674,6 +674,7 @@ def __init__(
         test_stat="qtilde",
         ntoys=2000,
         track_progress=True,
+        skip_failing_toys = False,
     ):
         r"""
         Toy-based Calculator.
@@ -704,6 +705,7 @@ def __init__(
             ~pyhf.infer.calculators.ToyCalculator: The calculator for toy-based quantities.
 
         """
+        self.skip_failing_toys = skip_failing_toys
         self.ntoys = ntoys
         self.data = data
         self.pdf = pdf
@@ -753,6 +755,9 @@ def distributions(self, poi_test, track_progress=None):
             Tuple (~pyhf.infer.calculators.EmpiricalDistribution): The distributions under the hypotheses.
 
         """
+
+        print('skip?',self.skip_failing_toys)
+
         tensorlib, _ = get_backend()
         sample_shape = (self.ntoys,)
 
@@ -791,29 +796,47 @@ def distributions(self, poi_test, track_progress=None):
 
         signal_teststat = []
         for sample in tqdm.tqdm(signal_sample, **tqdm_options, desc='Signal-like'):
-            signal_teststat.append(
-                teststat_func(
-                    poi_test,
-                    sample,
-                    self.pdf,
-                    self.init_pars,
-                    self.par_bounds,
-                    self.fixed_params,
+            try: 
+                value = teststat_func(
+                        poi_test,
+                        sample,
+                        self.pdf,
+                        self.init_pars,
+                        self.par_bounds,
+                        self.fixed_params,
+                )
+            except RuntimeError:
+                if self.skip_failing_toys:
+                    value = None
+                else:
+                    raise
+
+            if (value is not None) and (tensorlib.isfinite(value)):
+                signal_teststat.append(
+                    value    
                 )
-            )
 
         bkg_teststat = []
         for sample in tqdm.tqdm(bkg_sample, **tqdm_options, desc='Background-like'):
-            bkg_teststat.append(
-                teststat_func(
-                    poi_test,
-                    sample,
-                    self.pdf,
-                    self.init_pars,
-                    self.par_bounds,
-                    self.fixed_params,
+            try: 
+                value = teststat_func(
+                        poi_test,
+                        sample,
+                        self.pdf,
+                        self.init_pars,
+                        self.par_bounds,
+                        self.fixed_params,
+                )
+            except RuntimeError:
+                if self.skip_failing_toys:
+                    value = None
+                else:
+                    raise
+
+            if (value is not None) and (tensorlib.isfinite(value)):
+                bkg_teststat.append(
+                    value
                 )
-            )
 
         s_plus_b = EmpiricalDistribution(tensorlib.astensor(signal_teststat))
         b_only = EmpiricalDistribution(tensorlib.astensor(bkg_teststat))