Updating sympy.stats.crv_types for extreme value distributions

sympy/core/tests/test_args.py

@@ -1341,9 +1341,13 @@ def test_sympy__stats__crv_types__GammaDistribution():
     from sympy.stats.crv_types import GammaDistribution
     assert _test_args(GammaDistribution(1, 1))
 
-def test_sympy__stats__crv_types__GumbelDistribution():
-    from sympy.stats.crv_types import GumbelDistribution
-    assert _test_args(GumbelDistribution(1, 1))
+def test_sympy__stats__crv_types__GumbelDistributionMinimum():
+    from sympy.stats.crv_types import GumbelDistributionMinimum
+    assert _test_args(GumbelDistributionMinimum(1, 1))
+
+def test_sympy__stats__crv_types__GumbelDistributionMaximum():
+    from sympy.stats.crv_types import GumbelDistributionMaximum
+    assert _test_args(GumbelDistributionMaximum(1, 1))
 
 def test_sympy__stats__crv_types__GompertzDistribution():
     from sympy.stats.crv_types import GompertzDistribution

sympy/stats/crv_types.py

@@ -1441,46 +1441,78 @@ def GammaInverse(name, a, b):
     return rv(name, GammaInverseDistribution, (a, b))
 
 #-------------------------------------------------------------------------------
-# Gumbel distribution --------------------------------------------------------
+# Gumbel distribution (Maximum and Minimum)--------------------------------------------------------
 
 
-class GumbelDistribution(SingleContinuousDistribution):
+class GumbelDistributionMaximum(SingleContinuousDistribution):
     _argnames = ('beta', 'mu')
 
     set = Interval(-oo, oo)
 
+    @staticmethod
+    def check(beta, mu):
+        _value_check(beta > 0, "beta must be positive")
+
     def pdf(self, x):
         beta, mu = self.beta, self.mu
         z = (x - mu)/beta
         return (1/beta)*exp(-(z + exp(-z)))
 
     def _cdf(self, x):
         beta, mu = self.beta, self.mu
-        return exp(-exp((mu - x)/beta))
+        z = (x - mu)/beta
+        return exp(-exp(-z))
 
     def _characteristic_function(self, t):
         return gamma(1 - I*self.beta*t) * exp(I*self.mu*t)
 
     def _moment_generating_function(self, t):
         return gamma(1 - self.beta*t) * exp(I*self.mu*t)
 
-def Gumbel(name, beta, mu):
+class GumbelDistributionMinimum(SingleContinuousDistribution):
+    _argnames = ('beta', 'mu')
+
+    set = Interval(-oo, oo)
+
+    @staticmethod
+    def check(beta, mu):
+        _value_check(beta > 0, "beta must be positive")
+
+    def pdf(self, x):
+        beta, mu = self.beta, self.mu
+        z = (x - mu)/beta
+        return (1/beta)*exp(z - exp(z))
+
+    def _cdf(self, x):
+        beta, mu = self.beta, self.mu
+        z = (x - mu)/beta
+        return 1 - exp(-exp(z))
+
+def Gumbel(name, beta, mu, **kwargs):
     r"""
     Create a Continuous Random Variable with Gumbel distribution.
 
-    The density of the Gumbel distribution is given by
+    The density of the Gumbel distribution is given by,
 
+    For Maximum
     .. math::
         f(x) := \dfrac{1}{\beta} \exp \left( -\dfrac{x-\mu}{\beta}
                 - \exp \left( -\dfrac{x - \mu}{\beta} \right) \right)
 
     with :math:`x \in [ - \infty, \infty ]`.
 
+    For Minimum
+    .. math::
+        f(x) := \frac{e^{- e^{\frac{- \mu + x}{\beta}}
+                + \frac{- \mu + x}{\beta}}}{\beta}
+
     Parameters
     ==========
 
     mu: Real number, 'mu' is a location
     beta: Real number, 'beta > 0' is a scale
+    for_min: Boolean, optional, False, by default
+        For enabling the minimum distribution
 
     Returns
     ==========
@@ -1492,22 +1524,30 @@ def Gumbel(name, beta, mu):
     >>> from sympy.stats import Gumbel, density, E, variance, cdf
     >>> from sympy import Symbol, simplify, pprint
     >>> x = Symbol("x")
+    >>> y = Symbol("y")
     >>> mu = Symbol("mu")
     >>> beta = Symbol("beta", positive=True)
     >>> X = Gumbel("x", beta, mu)
+    >>> Y = Gumbel("y", beta, mu, for_min=True)
     >>> density(X)(x)
     exp(-exp(-(-mu + x)/beta) - (-mu + x)/beta)/beta
     >>> cdf(X)(x)
-    exp(-exp((mu - x)/beta))
+    exp(-exp(-(-mu + x)/beta))
+    >>> density(Y)(y)
+    exp(-exp((-mu + y)/beta) + (-mu + y)/beta)/beta
 
     References
     ==========
 
     .. [1] http://mathworld.wolfram.com/GumbelDistribution.html
     .. [2] https://en.wikipedia.org/wiki/Gumbel_distribution
+    .. [3] http://www.mathwave.com/help/easyfit/html/analyses/distributions/gumbel_max.html
+    .. [4] http://www.mathwave.com/help/easyfit/html/analyses/distributions/gumbel_min.html
 
     """
-    return rv(name, GumbelDistribution, (beta, mu))
+    if kwargs.get('for_min', False):
+        return rv(name, GumbelDistributionMinimum, (beta, mu))
+    return rv(name, GumbelDistributionMaximum, (beta, mu))
 
 #-------------------------------------------------------------------------------
 # Gompertz distribution --------------------------------------------------------

sympy/stats/tests/test_continuous_rv.py

@@ -446,9 +446,12 @@ def test_gumbel():
     beta = Symbol("beta", positive=True)
     mu = Symbol("mu")
     x = Symbol("x")
+    y = Symbol("y")
     X = Gumbel("x", beta, mu)
+    Y = Gumbel("y", beta, mu, for_min=True)
     assert str(density(X)(x)) == 'exp(-exp(-(-mu + x)/beta) - (-mu + x)/beta)/beta'
-    assert cdf(X)(x) == exp(-exp((mu - x)/beta))
+    assert str(density(Y)(y)) == 'exp(-exp((-mu + y)/beta) + (-mu + y)/beta)/beta'
+    assert str(cdf(X)(x)) == 'exp(-exp(-(-mu + x)/beta))'
 
 
 def test_kumaraswamy():