diff --git a/lshmm/core.py b/lshmm/core.py
index b8bd86d..e912959 100644
--- a/lshmm/core.py
+++ b/lshmm/core.py
@@ -302,6 +302,66 @@ def get_emission_probability_haploid(ref_allele, query_allele, site, emission_ma
             return emission_matrix[site, 1]
 
 
+@jit.numba_njit
+def get_emission_probability_haploid_hkylike(ref_allele, query_allele, site, emission_matrix):
+    """
+    Return the emission probability at a specified site for the haploid case,
+    given an emission probability matrix.
+
+    The emission probability matrix is an array of size (m, 4),
+    where m = number of sites.
+
+    :param int ref_allele: Reference allele.
+    :param int query_allele: Query allele.
+    :param int site: Site index.
+    :param numpy.ndarray emission_matrix: Emission probability matrix.
+    :return: Emission probability.
+    :rtype: float
+    """
+    if ref_allele == MISSING:
+        raise ValueError("Reference allele cannot be MISSING.")
+    if query_allele == NONCOPY:
+        raise ValueError("Query allele cannot be NONCOPY.")
+    if emission_matrix.shape[1] != 2:
+        raise ValueError("Emission probability matrix has incorrect shape.")
+    if ref_allele == NONCOPY:
+        return 0.0
+    elif query_allele == MISSING:
+        return 1.0
+    else:
+        return emission_matrix[ref_allele, query_allele]
+
+
+@jit.numba_njit
+def get_emission_matrix_hkylike(mu, kappa=None):
+    """
+    Return an emission probability matrix that allows for
+    differences between transition and transversion rates.
+
+    When `kappa` is set to None, it is equivalent to setting it to 1.
+
+    :param float mu: Probability of mutation to any allele.
+    :param float kappa: Transition-to-transversion rate ratio.
+    """
+    if kappa <= 0:
+        raise ValueError("Ts/tv ratio must be positive.")
+    # Assume that ACGT are encoded as 0 to 3.
+    num_alleles = 4
+    emission_matrix = np.zeros((num_alleles, num_alleles), dtype=np.float64) - 1
+    for i in range(num_alleles):
+        for j in range(num_alleles):
+            if i == j:
+                emission_matrix[i, j] = 1 - mu
+            else:
+                emission_matrix[i, j] = mu / 3
+                if kappa is not None:
+                    # Transitions: A <-> G, C <-> T.
+                    is_transition = (i in [0, 2] and j in [0, 2]) or (i in [1, 3] and j in [1, 3])
+                    if is_transition:
+                        emission_matrix[i, j] *= kappa
+    return emission_matrix
+
+
 # Functions to assign emission probabilities for diploid LS HMM.
 @jit.numba_njit
 def get_emission_matrix_diploid(mu, num_sites, num_alleles, scale_mutation_rate):