diff --git a/cara/tests/test_sampleable_distribution.py b/cara/tests/test_sampleable_distribution.py
index b3887763..e3801c7e 100644
--- a/cara/tests/test_sampleable_distribution.py
+++ b/cara/tests/test_sampleable_distribution.py
@@ -3,8 +3,8 @@ import numpy.testing as npt
 import pytest
 
 from cara.monte_carlo import sampleable
-# TODO: seed deterministically the random number generators, here (to
-# avoid random issues with tests)
+# TODO: seed better the random number generators
+np.random.seed(2000)
 
 @pytest.mark.parametrize(
     "mean, std",[
@@ -17,12 +17,14 @@ def test_normal(mean, std):
     sample_size = 2000000
     samples = sampleable.Normal(mean, std).generate_samples(sample_size)
     histogram, bins = np.histogram(samples,bins=100, density=True)
-    x = (bins[1:]+bins[:-1])/2
-    exact_dist = 1/(np.sqrt(2*np.pi)*std) * np.exp(-((x-mean)/std)**2/2)
+    selected_bins,selected_histogram = zip(*[(b,h) for b,h in zip(
+                (bins[1:]+bins[:-1])/2,histogram) if b>=0.25 and b<=1.75])
+    exact_dist = 1/(np.sqrt(2*np.pi)*std) * np.exp(
+                    -((np.array(selected_bins)-mean)/std)**2/2)
 
     assert len(samples) == sample_size
-    npt.assert_allclose([samples.mean(), samples.std()], [mean, std], atol=mean/100)
-    npt.assert_allclose(histogram, exact_dist, atol=exact_dist.mean()/20)
+    npt.assert_allclose([samples.mean(), samples.std()], [mean, std], rtol=0.01)
+    npt.assert_allclose(selected_histogram, exact_dist, rtol=0.02)
 
 
 @pytest.mark.parametrize(
@@ -37,17 +39,19 @@ def test_lognormal(mean_gaussian, std_gaussian):
     samples = sampleable.LogNormal(mean_gaussian, std_gaussian
                                 ).generate_samples(sample_size)
     histogram, bins = np.histogram(samples,bins=50, density=True)
-    x = (bins[1:]+bins[:-1])/2
-    exact_dist = ( 1/(x*np.sqrt(2*np.pi)*std_gaussian) * 
-                   np.exp(-((np.log(x)-mean_gaussian)/std_gaussian)**2/2) )
+    selected_bins,selected_histogram = zip(*[(b,h) for b,h in zip(
+                (bins[1:]+bins[:-1])/2,histogram) if b>=0.4 and b<=0.6])
+    selected_bins = np.array(selected_bins)
+    exact_dist = ( 1/(selected_bins*np.sqrt(2*np.pi)*std_gaussian) *
+            np.exp(-((np.log(selected_bins)-mean_gaussian)/std_gaussian)**2/2) )
     exact_mean = np.exp(mean_gaussian + std_gaussian**2/2)
     exact_std = np.sqrt( (np.exp(std_gaussian**2)-1) *
                          np.exp(2*mean_gaussian + std_gaussian**2) )
 
     assert len(samples) == sample_size
     npt.assert_allclose([samples.mean(), samples.std()],
-                        [exact_mean, exact_std], atol=exact_mean/100)
-    npt.assert_allclose(histogram, exact_dist, atol=exact_dist.mean()/20)
+                        [exact_mean, exact_std], rtol=0.01)
+    npt.assert_allclose(selected_histogram, exact_dist, rtol=0.02)
 
 
 @pytest.mark.parametrize(
@@ -71,13 +75,36 @@ def test_custom(use_kernel):
         samples = sampleable.CustomKernel(variable, frequencies,
                                     kernel_bandwidth=0.1
                                     ).generate_samples(sample_size)
-        tolerance = max_function/10
     else:
         samples = sampleable.Custom((0, 10), function, max_function
                                     ).generate_samples(sample_size)
-        tolerance = max_function/50
 
     histogram, bins = np.histogram(samples, bins=100, density=True)
-    correct_dist = function((bins[1:]+bins[:-1])/2)
+    selected_bins,selected_histogram = zip(*[(b,h) for b,h in zip(
+                (bins[1:]+bins[:-1])/2,histogram) if b>=1 and b<=9])
+    correct_dist = function(np.array(selected_bins))
     assert len(samples) == sample_size
-    npt.assert_allclose(histogram, correct_dist, atol=tolerance)
+    npt.assert_allclose(selected_histogram, correct_dist, rtol=0.05)
+
+
+def test_logcustomkernel():
+    # test that the sample has approximately the right distribution
+    # function, for the LogCustomKernel.
+    # the distribution function is an inverted parabola vs. the log of
+    # the variable (normalized)
+    norm = 500/3.
+    function = lambda x: (-(5 - x)**2 + 25)/norm
+    sample_size = 2000000
+
+    log_variable = np.linspace(0.1,9.9,100)
+    frequencies = function(log_variable)
+    samples = sampleable.LogCustomKernel(log_variable, frequencies,
+                                kernel_bandwidth=0.1
+                                ).generate_samples(sample_size)
+
+    histogram, bins = np.histogram(np.log10(samples), bins=100, density=True)
+    selected_bins,selected_histogram = zip(*[(b,h) for b,h in zip(
+                (bins[1:]+bins[:-1])/2,histogram) if b>=1 and b<=9])
+    correct_dist = function(np.array(selected_bins))
+    assert len(samples) == sample_size
+    npt.assert_allclose(selected_histogram, correct_dist, rtol=0.05)