chore: moments and entropy were extra and removed

numpyro/distributions/continuous.py

@@ -2986,31 +2986,6 @@ def sample(self, key, sample_shape=()):
         samples = self.icdf(u)
         return samples
 
-    def _kth_moment(self, k):
-        Z = jnp.exp(self._logZ)
-
-        def index_eq_neg1():
-            return (jnp.log(self.high) - jnp.log(self.low)) / Z
-
-        def index_neq_neg1():
-            power_index = k + self.alpha + 1.0
-            return (
-                jnp.power(self.high, power_index) - jnp.power(self.low, power_index)
-            ) / ((power_index) * Z)
-
-        return jnp.where(
-            jnp.equal(self.alpha + k, -1.0), index_eq_neg1(), index_neq_neg1()
-        )
-
-    @lazy_property
-    def mean(self):
-        return self._kth_moment(1)
-
-    @lazy_property
-    def variance(self):
-        moment2 = self._kth_moment(2)
-        return moment2 - jnp.square(self.mean)
-
 
 class LowerTruncatedPowerLaw(Distribution):
     r"""Lower truncated power law distribution with :math:`\alpha` index.
@@ -3086,36 +3061,3 @@ def sample(self, key, sample_shape=()):
         u = random.uniform(key, sample_shape + self.batch_shape)
         samples = self.icdf(u)
         return samples
-
-    def _kth_moment(self, k):
-        return jnp.where(
-            jnp.less(k, self.alpha - 1),
-            (self.alpha - 1) / (self.alpha - 1 - k) * jnp.power(self.low, k),
-            jnp.inf,
-        )
-
-    @lazy_property
-    def mean(self):
-        return self._kth_moment(1)
-
-    @lazy_property
-    def variance(self):
-        return self._kth_moment(2) - jnp.square(self.mean)
-
-    def entropy(self):
-        # The simplified expression for the entorpy is,
-        # H(x) = (alpha-1)log(a) - log(a-1)
-        #        + alpha(alpha-1)a^(alpha-1)\int_{a}^{\infty}x^{-alpha}log(x)dx
-        # The integral term can be reshaped into a lower incomplete gamma function.
-        # After simplification, we get the following expression.
-        # H(x) = (alpha-1)log(a) - log(a-1)
-        #        + (alpha/(alpha-1))a^(alpha-1)(1-gamma(2, (alpha-1)log(a)))
-        # I followed the definition of lower incomplete gamma function from wikipedia.
-        # https://en.wikipedia.org/wiki/Incomplete_gamma_function#Definition
-        # In the very same wikipedia article there was a recursive formula,
-        # https://en.wikipedia.org/wiki/Incomplete_gamma_function#Properties
-        # which I used to simplify the expression. It gave me the following expression.
-        # H(x) = log(a) - log(alpha-1) + (alpha/(alpha-1))(a^(alpha-1) + 1)
-        Hx = jnp.log(self.low) - jnp.log(self.alpha - 1)
-        Hx += self.alpha / (self.alpha - 1) * (jnp.power(self.low, self.alpha - 1) + 1)
-        return Hx