diff --git a/numcosmo/math/ncm_stats_dist.c b/numcosmo/math/ncm_stats_dist.c
index 5808fdba..2d769423 100644
--- a/numcosmo/math/ncm_stats_dist.c
+++ b/numcosmo/math/ncm_stats_dist.c
@@ -709,7 +709,7 @@ _ncm_stats_dist_prepare (NcmStatsDist *sd)
       break;
   }
 
-  if (self->n_obs < self->d)
+  if (self->n_obs <= self->d)
     g_error ("_ncm_stats_dist_prepare: the sample is too small.");
 
   sd_class->prepare_kernel (sd, self->sample_array);
diff --git a/numcosmo/math/ncm_stats_dist_kernel.c b/numcosmo/math/ncm_stats_dist_kernel.c
index 7db1b9a4..3135d51b 100644
--- a/numcosmo/math/ncm_stats_dist_kernel.c
+++ b/numcosmo/math/ncm_stats_dist_kernel.c
@@ -254,7 +254,7 @@ ncm_stats_dist_kernel_class_init (NcmStatsDistKernelClass *klass)
                                    g_param_spec_uint ("dimension",
                                                       NULL,
                                                       "Kernel dimension",
-                                                      2, G_MAXUINT, 2,
+                                                      1, G_MAXUINT, 2,
                                                       G_PARAM_READWRITE | G_PARAM_CONSTRUCT_ONLY | G_PARAM_STATIC_NAME | G_PARAM_STATIC_BLURB));
 
   sd_class->set_dim                = &_ncm_stats_dist_kernel_set_dim;
diff --git a/numcosmo/math/ncm_stats_vec.c b/numcosmo/math/ncm_stats_vec.c
index 332a87f7..577a626d 100644
--- a/numcosmo/math/ncm_stats_vec.c
+++ b/numcosmo/math/ncm_stats_vec.c
@@ -248,7 +248,7 @@ _ncm_stats_vec_constructed (GObject *object)
     switch (svec->t)
     {
       case NCM_STATS_VEC_COV:
-        g_assert_cmpuint (svec->len, >, 1);
+        g_assert_cmpuint (svec->len, >, 0);
         g_assert (svec->cov == NULL);
 
         svec->cov    = ncm_matrix_new (svec->len, svec->len);
diff --git a/tests/test_ncm_fit_esmcmc.c b/tests/test_ncm_fit_esmcmc.c
index fac69887..c9a7f9a3 100644
--- a/tests/test_ncm_fit_esmcmc.c
+++ b/tests/test_ncm_fit_esmcmc.c
@@ -123,7 +123,7 @@ main (gint argc, gchar *argv[])
 void
 test_ncm_fit_esmcmc_new_apes (TestNcmFitESMCMC *test, gconstpointer pdata)
 {
-  const gint dim                      = test->dim = g_test_rand_int_range (2, 4);
+  const gint dim                      = test->dim = g_test_rand_int_range (1, 4);
   const gint nwalkers                 = 100 * test->dim;
   NcmRNG *rng                         = ncm_rng_seeded_new (NULL, g_test_rand_int ());
   NcmDataGaussCovMVND *data_mvnd      = ncm_data_gauss_cov_mvnd_new_full (dim, 2.0e-2, 5.0e-2, 30.0, 1.0, 2.0, rng);
@@ -273,7 +273,7 @@ test_ncm_fit_esmcmc_new_apes (TestNcmFitESMCMC *test, gconstpointer pdata)
 void
 test_ncm_fit_esmcmc_new_stretch (TestNcmFitESMCMC *test, gconstpointer pdata)
 {
-  const gint dim                      = test->dim = g_test_rand_int_range (2, 4);
+  const gint dim                      = test->dim = g_test_rand_int_range (1, 4);
   const gint nwalkers                 = 10 * g_test_rand_int_range (2, 5);
   NcmRNG *rng                         = ncm_rng_seeded_new (NULL, g_test_rand_int ());
   NcmDataGaussCovMVND *data_mvnd      = ncm_data_gauss_cov_mvnd_new_full (dim, 1.0e-2, 2.0e-2, 30.0, 1.0, 2.0, rng);
diff --git a/tests/test_ncm_stats_dist.c b/tests/test_ncm_stats_dist.c
index 831129d3..fe22f1f4 100644
--- a/tests/test_ncm_stats_dist.c
+++ b/tests/test_ncm_stats_dist.c
@@ -159,7 +159,7 @@ main (gint argc, gchar *argv[])
 static void
 test_ncm_stats_dist_new_kde_gauss (TestNcmStatsDist *test, gconstpointer pdata)
 {
-  const guint dim                    = g_test_rand_int_range (2, 4);
+  const guint dim                    = g_test_rand_int_range (1, 4);
   NcmStatsDistKernelGauss *sdk_gauss = ncm_stats_dist_kernel_gauss_new (dim);
   NcmStatsDistKDE *sdkde             = ncm_stats_dist_kde_new (NCM_STATS_DIST_KERNEL (sdk_gauss), NCM_STATS_DIST_CV_NONE);
   NcmStatsDistKDECovType cov_type    = GPOINTER_TO_INT (pdata);
@@ -210,7 +210,7 @@ static void
 test_ncm_stats_dist_new_kde_studentt (TestNcmStatsDist *test, gconstpointer pdata)
 {
   const gdouble nu                = g_test_rand_double_range (3.0, 5.0);
-  const guint dim                 = g_test_rand_int_range (2, 4);
+  const guint dim                 = g_test_rand_int_range (1, 4);
   NcmStatsDistKernelST *sdk_st    = ncm_stats_dist_kernel_st_new (dim, nu);
   NcmStatsDistKDE *sdkde          = ncm_stats_dist_kde_new (NCM_STATS_DIST_KERNEL (sdk_st), NCM_STATS_DIST_CV_NONE);
   NcmStatsDistKDECovType cov_type = GPOINTER_TO_INT (pdata);
@@ -260,7 +260,7 @@ test_ncm_stats_dist_new_kde_studentt (TestNcmStatsDist *test, gconstpointer pdat
 static void
 test_ncm_stats_dist_new_vkde_gauss (TestNcmStatsDist *test, gconstpointer pdata)
 {
-  const guint dim                    = g_test_rand_int_range (2, 4);
+  const guint dim                    = g_test_rand_int_range (1, 4);
   NcmStatsDistKernelGauss *sdk_gauss = ncm_stats_dist_kernel_gauss_new (dim);
   NcmStatsDistVKDE *sdvkde           = ncm_stats_dist_vkde_new (NCM_STATS_DIST_KERNEL (sdk_gauss), NCM_STATS_DIST_CV_NONE);
   NcmStatsDistKDECovType cov_type    = GPOINTER_TO_INT (pdata);
@@ -312,7 +312,7 @@ static void
 test_ncm_stats_dist_new_vkde_studentt (TestNcmStatsDist *test, gconstpointer pdata)
 {
   const gdouble nu                = g_test_rand_double_range (3.0, 5.0);
-  const guint dim                 = g_test_rand_int_range (2, 4);
+  const guint dim                 = g_test_rand_int_range (1, 4);
   NcmStatsDistKernelST *sdk_st    = ncm_stats_dist_kernel_st_new (dim, nu);
   NcmStatsDistVKDE *sdvkde        = ncm_stats_dist_vkde_new (NCM_STATS_DIST_KERNEL (sdk_st), NCM_STATS_DIST_CV_NONE);
   NcmStatsDistKDECovType cov_type = GPOINTER_TO_INT (pdata);
diff --git a/tests/test_ncm_stats_dist_kernel.c b/tests/test_ncm_stats_dist_kernel.c
index 2fea5dbb..e4b72b18 100644
--- a/tests/test_ncm_stats_dist_kernel.c
+++ b/tests/test_ncm_stats_dist_kernel.c
@@ -79,15 +79,15 @@ typedef struct _TestNcmStatsDistKernelFunc
 
 static TestNcmStatsDistKernelFunc constructors[TEST_NCM_STATS_DIST_KERNEL_CONSTRUCTORS_LEN] = {
   {"gauss", &test_ncm_stats_dist_kernel_new_gauss},
-  {"st",  &test_ncm_stats_dist_kernel_new_st}
+  {"st",    &test_ncm_stats_dist_kernel_new_st}
 };
 
 static TestNcmStatsDistKernelFunc tests[TEST_NCM_STATS_DIST_KERNEL_TESTS_LEN] = {
-  {"dim",   &test_ncm_stats_dist_kernel_dim},
-  {"band",        &test_ncm_stats_dist_kernel_bandwidth},
-  {"gauss/norm",        &test_ncm_stats_dist_kernel_norm},
-  {"sum",         &test_ncm_stats_dist_kernel_sum},
-  {"sample",      &test_ncm_stats_dist_kernel_sample},
+  {"dim",        &test_ncm_stats_dist_kernel_dim},
+  {"band",       &test_ncm_stats_dist_kernel_bandwidth},
+  {"gauss/norm", &test_ncm_stats_dist_kernel_norm},
+  {"sum",        &test_ncm_stats_dist_kernel_sum},
+  {"sample",     &test_ncm_stats_dist_kernel_sample},
 };
 
 gint
@@ -129,7 +129,7 @@ main (gint argc, gchar *argv[])
 static void
 test_ncm_stats_dist_kernel_new_gauss (TestNcmStatsDistKernel *test, gconstpointer pdata)
 {
-  const guint dim                    = g_test_rand_int_range (2, 4);
+  const guint dim                    = g_test_rand_int_range (1, 4);
   NcmStatsDistKernelGauss *sdk_gauss = ncm_stats_dist_kernel_gauss_new (dim);
 
   test->dim         = dim;
@@ -151,7 +151,7 @@ static void
 test_ncm_stats_dist_kernel_new_st (TestNcmStatsDistKernel *test, gconstpointer pdata)
 {
   const gdouble nu             = g_test_rand_double_range (3.0, 5.0);
-  const guint dim              = g_test_rand_int_range (2, 4);
+  const guint dim              = g_test_rand_int_range (1, 4);
   NcmStatsDistKernelST *sdk_st = ncm_stats_dist_kernel_st_new (dim, nu);
 
   test->dim         = dim;