Implement Maxwell Distribution

docs/api_reference.rst

@@ -29,6 +29,7 @@ Distributions
    :toctree: generated/
 
    Chi
+   Maxwell
    DiscreteMarkovChain
    GeneralizedPoisson
    GenExtreme

pymc_experimental/distributions/__init__.py

@@ -17,7 +17,7 @@
 Experimental probability distributions for stochastic nodes in PyMC.
 """
 
-from pymc_experimental.distributions.continuous import Chi, GenExtreme
+from pymc_experimental.distributions.continuous import Chi, GenExtreme, Maxwell
 from pymc_experimental.distributions.discrete import GeneralizedPoisson, Skellam
 from pymc_experimental.distributions.histogram_utils import histogram_approximation
 from pymc_experimental.distributions.multivariate import R2D2M2CP
@@ -30,4 +30,5 @@
     "R2D2M2CP",
     "histogram_approximation",
     "Chi",
+    "Maxwell",
 ]

pymc_experimental/distributions/continuous.py

@@ -280,3 +280,68 @@ def __new__(cls, name, nu, **kwargs):
     @classmethod
     def dist(cls, nu, **kwargs):
         return CustomDist.dist(nu, dist=cls.chi_dist, class_name="Chi", **kwargs)
+
+
+class Maxwell:
+    R"""
+    The Maxwell-Boltzmann distribution
+
+    The pdf of this distribution is
+
+    .. math::
+
+       f(x \mid a) = {\displaystyle {\sqrt {\frac {2}{\pi }}}\,{\frac {x^{2}}{a^{3}}}\,\exp \left({\frac {-x^{2}}{2a^{2}}}\right)}
+
+    Read more about it on `Wikipedia <https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution>`_
+
+    .. plot::
+        :context: close-figs
+
+        import matplotlib.pyplot as plt
+        import numpy as np
+        import scipy.stats as st
+        import arviz as az
+        plt.style.use('arviz-darkgrid')
+        x = np.linspace(0, 20, 200)
+        for a in [1, 2, 5]:
+            pdf = st.maxwell.pdf(x, scale=a)
+            plt.plot(x, pdf, label=r'$a$ = {}'.format(a))
+        plt.xlabel('x', fontsize=12)
+        plt.ylabel('f(x)', fontsize=12)
+        plt.legend(loc=1)
+        plt.show()
+
+    ========  =========================================================================
+    Support   :math:`x \in (0, \infty)`
+    Mean      :math:`2a \sqrt{\frac{2}{\pi}}`
+    Variance  :math:`\frac{a^2(3 \pi - 8)}{\pi}`
+    ========  =========================================================================
+
+    Parameters
+    ----------
+    a : tensor_like of float
+        Scale parameter (a > 0).
+
+    """
+
+    @staticmethod
+    def maxwell_dist(a: TensorVariable, size: TensorVariable) -> TensorVariable:
+        return Chi.dist(nu=3, size=size) * a
+
+    def __new__(cls, name, a, **kwargs):
+        return CustomDist(
+            name,
+            a,
+            dist=cls.maxwell_dist,
+            class_name="Maxwell",
+            **kwargs,
+        )
+
+    @classmethod
+    def dist(cls, a, **kwargs):
+        return CustomDist.dist(
+            a,
+            dist=cls.maxwell_dist,
+            class_name="Maxwell",
+            **kwargs,
+        )

pymc_experimental/tests/distributions/test_continuous.py

@@ -33,7 +33,7 @@
 )
 
 # the distributions to be tested
-from pymc_experimental.distributions import Chi, GenExtreme
+from pymc_experimental.distributions import Chi, GenExtreme, Maxwell
 
 
 class TestGenExtremeClass:
@@ -159,3 +159,26 @@ def test_logcdf(self):
             {"nu": Rplus},
             lambda value, nu: sp.chi.logcdf(value, df=nu),
         )
+
+
+class TestMaxwell:
+    """
+    Wrapper class so that tests of experimental additions can be dropped into
+    PyMC directly on adoption.
+    """
+
+    def test_logp(self):
+        check_logp(
+            Maxwell,
+            Rplus,
+            {"a": Rplus},
+            lambda value, a: sp.maxwell.logpdf(value, scale=a),
+        )
+
+    def test_logcdf(self):
+        check_logcdf(
+            Maxwell,
+            Rplus,
+            {"a": Rplus},
+            lambda value, a: sp.maxwell.logcdf(value, scale=a),
+        )