diff --git a/pymc/distributions/continuous.py b/pymc/distributions/continuous.py
index 75a75b07c1..fa4c056f93 100644
--- a/pymc/distributions/continuous.py
+++ b/pymc/distributions/continuous.py
@@ -57,6 +57,7 @@
 from pytensor.tensor.var import TensorConstant
 
 from pymc.logprob.abstract import _logcdf_helper, _logprob_helper
+from pymc.logprob.basic import icdf
 
 try:
     from polyagamma import polyagamma_cdf, polyagamma_pdf, random_polyagamma
@@ -856,6 +857,11 @@ def logcdf(value, loc, sigma):
             msg="sigma > 0",
         )
 
+    def icdf(value, loc, sigma):
+        res = icdf(Normal.dist(loc, sigma), (value + 1.0) / 2.0)
+        res = check_icdf_value(res, value)
+        return res
+
 
 class WaldRV(RandomVariable):
     name = "wald"
@@ -1714,12 +1720,17 @@ def logcdf(value, mu, sigma):
             -np.inf,
             normal_lcdf(mu, sigma, pt.log(value)),
         )
+
         return check_parameters(
             res,
             sigma > 0,
             msg="sigma > 0",
         )
 
+    def icdf(value, mu, sigma):
+        res = pt.exp(icdf(Normal.dist(mu, sigma), value))
+        return res
+
 
 Lognormal = LogNormal
 
@@ -2121,6 +2132,15 @@ def logcdf(value, loc, beta):
             msg="beta > 0",
         )
 
+    def icdf(value, loc, beta):
+        res = loc + beta * pt.tan(np.pi * (value) / 2.0)
+        res = check_icdf_value(res, value)
+        return check_parameters(
+            res,
+            beta > 0,
+            msg="beta > 0",
+        )
+
 
 class Gamma(PositiveContinuous):
     r"""
diff --git a/tests/distributions/test_continuous.py b/tests/distributions/test_continuous.py
index a4512b8a61..dccf6afeff 100644
--- a/tests/distributions/test_continuous.py
+++ b/tests/distributions/test_continuous.py
@@ -299,6 +299,11 @@ def test_half_normal(self):
             {"sigma": Rplus},
             lambda value, sigma: st.halfnorm.logcdf(value, scale=sigma),
         )
+        check_icdf(
+            pm.HalfNormal,
+            {"sigma": Rplus},
+            lambda q, sigma: st.halfnorm.ppf(q, scale=sigma),
+        )
 
     def test_chisquared_logp(self):
         check_logp(
@@ -502,6 +507,21 @@ def test_lognormal(self):
             {"mu": R, "sigma": Rplusbig},
             lambda value, mu, sigma: st.lognorm.logcdf(value, sigma, 0, np.exp(mu)),
         )
+        check_icdf(
+            pm.LogNormal,
+            {"mu": R, "tau": Rplusbig},
+            lambda q, mu, tau: floatX(st.lognorm.ppf(q, tau**-0.5, 0, np.exp(mu))),
+        )
+        # Because we exponentiate the normal quantile function, setting sigma >= 9.5
+        # return extreme values that results in relative errors above 4 digits
+        # we circumvent it by keeping it below or equal to 9.
+        custom_rplusbig = Domain([0, 0.5, 0.9, 0.99, 1, 1.5, 2, 9, np.inf])
+        check_icdf(
+            pm.LogNormal,
+            {"mu": R, "sigma": custom_rplusbig},
+            lambda q, mu, sigma: floatX(st.lognorm.ppf(q, sigma, 0, np.exp(mu))),
+            decimal=select_by_precision(float64=4, float32=3),
+        )
 
     def test_studentt_logp(self):
         check_logp(
@@ -567,6 +587,9 @@ def test_half_cauchy(self):
             {"beta": Rplusbig},
             lambda value, beta: st.halfcauchy.logcdf(value, scale=beta),
         )
+        check_icdf(
+            pm.HalfCauchy, {"beta": Rplusbig}, lambda q, beta: st.halfcauchy.ppf(q, scale=beta)
+        )
 
     def test_gamma_logp(self):
         check_logp(