diff --git a/docs/schemes/nist-pqc-round-3.rst b/docs/schemes/nist-pqc-round-3.rst
index eefde84..7a15397 100644
--- a/docs/schemes/nist-pqc-round-3.rst
+++ b/docs/schemes/nist-pqc-round-3.rst
@@ -60,7 +60,7 @@ NIST PQC Round 3 Finalists
 
     >>> from estimator import *
     >>> schemes.NTRUHPS2048509Enc
-    NTRUParameters(n=508, q=2048, Xs=D(σ=0.82), Xe=D(σ=0.71), m=508, tag='NTRUHPS2048509Enc', ntru_type='matrix')
+    NTRUParameters(n=508, q=2048, Xs=D(σ=0.82), Xe=T(p=127, m=127, n=508), m=508, tag='NTRUHPS2048509Enc', ntru_type='matrix')
     >>> NTRU.primal_bdd(schemes.NTRUHPS2048509Enc)
     rop: ≈2^131.1, red: ≈2^130.1, svp: ≈2^130.2, β: 357, η: 390, d: 916, tag: bdd
 
@@ -68,7 +68,7 @@ NIST PQC Round 3 Finalists
 
     >>> from estimator import *
     >>> schemes.NTRUHPS2048677Enc
-    NTRUParameters(n=676, q=2048, Xs=D(σ=0.82), Xe=D(σ=0.61), m=676, tag='NTRUHPS2048677Enc', ntru_type='matrix')
+    NTRUParameters(n=676, q=2048, Xs=D(σ=0.82), Xe=T(p=127, m=127, n=676), m=676, tag='NTRUHPS2048677Enc', ntru_type='matrix')
     >>> NTRU.primal_bdd(schemes.NTRUHPS2048677Enc)
     rop: ≈2^170.8, red: ≈2^169.6, svp: ≈2^169.9, β: 498, η: 533, d: 1179, tag: bdd
 
@@ -76,7 +76,7 @@ NIST PQC Round 3 Finalists
 
     >>> from estimator import *
     >>> schemes.NTRUHPS4096821Enc
-    NTRUParameters(n=820, q=4096, Xs=D(σ=0.82), Xe=D(σ=0.79), m=820, tag='NTRUHPS4096821Enc', ntru_type='matrix')
+    NTRUParameters(n=820, q=4096, Xs=D(σ=0.82), Xe=T(p=255, m=255, n=820), m=820, tag='NTRUHPS4096821Enc', ntru_type='matrix')
     >>> NTRU.primal_bdd(schemes.NTRUHPS4096821Enc)
     rop: ≈2^199.7, red: ≈2^198.7, svp: ≈2^198.6, β: 601, η: 636, d: 1485, tag: bdd
 
@@ -86,4 +86,4 @@ NIST PQC Round 3 Finalists
     >>> schemes.NTRUHRSS701Enc
     NTRUParameters(n=700, q=8192, Xs=D(σ=0.82), Xe=D(σ=0.82), m=700, tag='NTRUHRSS701', ntru_type='matrix')
     >>> NTRU.primal_bdd(schemes.NTRUHRSS701Enc)
-    rop: ≈2^158.7, red: ≈2^157.7, svp: ≈2^157.7, β: 454, η: 489, d: 1306, tag: bdd
\ No newline at end of file
+    rop: ≈2^158.7, red: ≈2^157.7, svp: ≈2^157.7, β: 454, η: 489, d: 1306, tag: bdd
diff --git a/estimator/nd.py b/estimator/nd.py
index 7c2fa5e..f31ef6a 100644
--- a/estimator/nd.py
+++ b/estimator/nd.py
@@ -239,6 +239,7 @@ class DiscreteGaussian(NoiseDistribution):
     gaussian_tail_prob: float = 1 - 2 * exp(-4 * pi)
 
     def __init__(self, stddev, mean=0, n=None):
+        stddev, mean = RR(stddev), RR(mean)
         b_val = oo if n is None else ceil(log(n, 2) * stddev)
         density = max(0.0, 1 - RR(1 / sigmaf(stddev)))  # NOTE: approximation that is accurate for large stddev.
 
@@ -288,7 +289,7 @@ def DiscreteGaussianAlpha(alpha, q, mean=0, n=None):
         >>> ND.DiscreteGaussianAlpha(alpha, q) == ND.DiscreteGaussian(ND.stddevf(alpha * q))
         True
     """
-    return DiscreteGaussian(RR(stddevf(alpha * q)), RR(mean), n)
+    return DiscreteGaussian(stddevf(alpha * q), mean, n)
 
 
 class CenteredBinomial(NoiseDistribution):
@@ -408,11 +409,11 @@ class SparseTernary(NoiseDistribution):
 
         >>> from estimator import *
         >>> ND.SparseTernary(10, n=100)
-        D(σ=0.45)
+        T(p=10, m=10, n=100)
         >>> ND.SparseTernary(10, 10, 100)
-        D(σ=0.45)
+        T(p=10, m=10, n=100)
         >>> ND.SparseTernary(10, 8, 100)
-        D(σ=0.42, μ=0.02)
+        T(p=10, m=8, n=100)
         >>> ND.SparseTernary(0, 0, 0).support_size()
         1
     """
@@ -509,6 +510,23 @@ def support_size(self, fraction=1.0):
         n, p, m = len(self), self.p, self.m
         return ceil(binomial(n, p) * binomial(n - p, m) * RR(fraction))
 
+    def __str__(self):
+        """
+        EXAMPLE::
+
+            >>> from estimator import *
+            >>> ND.SparseTernary(20, 20, n=100)
+            T(p=20, m=20, n=100)
+
+        """
+        if self.n:
+            return f"T(p={self.p}, m={self.m}, n={int(self.n)})"
+        else:
+            return f"T(p={int(self.p)}, m={int(self.m)})"
+
+    def __repr__(self):
+        return str(self)
+
 
 def SparseBinary(hw, n=None):
     """
diff --git a/estimator/ntru_parameters.py b/estimator/ntru_parameters.py
index c36f12b..d645efd 100644
--- a/estimator/ntru_parameters.py
+++ b/estimator/ntru_parameters.py
@@ -71,13 +71,12 @@ def updated(self, **kwds):
         EXAMPLE::
 
             >>> from estimator import *
-            >>> schemes.NTRUHPS2048509Enc  #doctest: +ELLIPSIS
-            NTRUParameters(n=508, q=2048, Xs=D(σ=0.82), Xe=D(σ=0.71), m=508, tag='NTRUHPS2048509Enc', ntru_type='ma...
+            >>> schemes.NTRUHPS2048509Enc
+            NTRUParameters(n=508, q=2048, Xs=D(σ=0.82), Xe=T(p=127, m=127, n=508), m=508, ...
             >>> schemes.NTRUHPS2048509Enc.possibly_overstretched
             False
-
-            >>> schemes.NTRUHPS2048509Enc.updated(q=16536)  #doctest: +ELLIPSIS
-            NTRUParameters(n=508, q=16536, Xs=D(σ=0.82), Xe=D(σ=0.71), ..., tag='NTRUHPS2048509Enc', ntru_type='matrix')
+            >>> schemes.NTRUHPS2048509Enc.updated(q=16536)
+            NTRUParameters(n=508, q=16536, Xs=D(σ=0.82), Xe=T(p=127, m=127, n=508), m=508, ...
             >>> schemes.NTRUHPS2048509Enc.updated(q=16536).possibly_overstretched
             True
         """