diff --git a/scipy/stats/_continuous_distns.py b/scipy/stats/_continuous_distns.py
index a9f679b9be50..390d97db3d03 100644
--- a/scipy/stats/_continuous_distns.py
+++ b/scipy/stats/_continuous_distns.py
@@ -4214,7 +4214,7 @@ class halflogistic_gen(rv_continuous):
     References
     ----------
     .. [1] Asgharzadeh et al (2011). "Comparisons of Methods of Estimation for the
-           Half-Logistic Distribution". Selcuk J. Appl. Math. 93-108. 
+           Half-Logistic Distribution". Selcuk J. Appl. Math. 93-108.
 
     %(example)s
 
@@ -4439,6 +4439,12 @@ def _cdf(self, x):
     def _ppf(self, q):
         return np.log(np.tan(np.pi*q/2.0))
 
+    def _sf(self, x):
+        return 2.0/np.pi*np.arctan(np.exp(-x))
+
+    def _isf(self, q):
+        return -np.log(np.tan(np.pi*q/2.0))
+
     def _stats(self):
         return 0, np.pi*np.pi/4, 0, 2
 
diff --git a/scipy/stats/tests/test_distributions.py b/scipy/stats/tests/test_distributions.py
index 26ee1655667d..0a75b976a76d 100644
--- a/scipy/stats/tests/test_distributions.py
+++ b/scipy/stats/tests/test_distributions.py
@@ -841,6 +841,29 @@ def test_pdf_norminvgauss(self):
             )
 
 
+class TestHypSecant:
+
+    # Reference values were computed with the mpmath expression
+    #     float((2/mp.pi)*mp.atan(mp.exp(-x)))
+    # and mp.dps = 50.
+    @pytest.mark.parametrize('x, reference',
+                             [(30, 5.957247804324683e-14),
+                              (50, 1.2278802891647964e-22)])
+    def test_sf(self, x, reference):
+        sf = stats.hypsecant.sf(x)
+        assert_allclose(sf, reference, rtol=5e-15)
+
+    # Reference values were computed with the mpmath expression
+    #     float(-mp.log(mp.tan((mp.pi/2)*p)))
+    # and mp.dps = 50.
+    @pytest.mark.parametrize('p, reference',
+                             [(1e-6, 13.363927852673998),
+                              (1e-12, 27.179438410639094)])
+    def test_isf(self, p, reference):
+        x = stats.hypsecant.isf(p)
+        assert_allclose(x, reference, rtol=5e-15)
+
+
 class TestNormInvGauss:
     def setup_method(self):
         np.random.seed(1234)
@@ -1873,14 +1896,14 @@ def test_rvs(self, c):
                               (1e10, -10.093986931748889),
                               (1e100, -113.71031611649761)])
     def test_entropy(self, c, ref):
-    
+
         # Reference values were calculated with mpmath
         # from mpmath import mp
         # mp.dps = 500
         # def loggamma_entropy_mpmath(c):
         #     c = mp.mpf(c)
         #     return float(mp.log(mp.gamma(c)) + c * (mp.one - mp.digamma(c)))
-        
+
         assert_allclose(stats.loggamma.entropy(c), ref, rtol=1e-14)
 
 
@@ -3415,7 +3438,6 @@ def test_t_inf_df_stats_entropy(self, df_infmask):
         assert_equal(res[df_infmask], res_ex_inf)
         assert_equal(res[~df_infmask], res_ex_noinf)
 
-
     def test_logpdf_pdf(self):
         # reference values were computed via the reference distribution, e.g.
         # mp.dps = 500; StudentT(df=df).logpdf(x), StudentT(df=df).pdf(x)
@@ -4020,6 +4042,7 @@ def test_cdf_ppf(self, x, p, a, b, c):
         ppf = stats.genexpon.ppf(p, a, b, c)
         assert_allclose(ppf, x, rtol=1e-14)
 
+
 class TestTruncexpon:
 
     def test_sf_isf(self):
@@ -5517,6 +5540,7 @@ def test_x_near_zeta(
             expected,
         )
 
+
 class TestArrayArgument:  # test for ticket:992
     def setup_method(self):
         np.random.seed(1234)