Add Gumbel distribution

preliz/distributions/__init__.py

@@ -8,6 +8,7 @@
     ChiSquared,
     Exponential,
     Gamma,
+    Gumbel,
     HalfCauchy,
     HalfNormal,
     HalfStudent,

preliz/distributions/continuous.py

@@ -564,6 +564,81 @@ def _fit_mle(self, sample, **kwargs):
         self._update(alpha, 1 / beta)
 
 
+class Gumbel(Continuous):
+    r"""
+    Gumbel distribution.
+
+    The pdf of this distribution is
+
+    .. math::
+
+       f(x \mid \mu, \beta) = \frac{1}{\beta}e^{-(z + e^{-z})}
+
+    where
+
+    .. math::
+
+        z = \frac{x - \mu}{\beta}
+
+    .. plot::
+        :context: close-figs
+
+        import arviz as az
+        from preliz import Gumbel
+        az.style.use('arviz-white')
+        mus = [0., 4., -1.]
+        betas = [1., 2., 4.]
+        for mu, beta in zip(mus, betas):
+            Gumbel(mu, beta).plot_pdf(support=(-10,20))
+
+    ========  ==========================================
+    Support   :math:`x \in \mathbb{R}`
+    Mean      :math:`\mu + \beta\gamma`, where :math:`\gamma` is the Euler-Mascheroni constant
+    Variance  :math:`\frac{\pi^2}{6} \beta^2`
+    ========  ==========================================
+
+    Parameters
+    ----------
+    mu : float
+        Location parameter.
+    beta : float
+        Scale parameter (beta > 0).
+    """
+
+    def __init__(self, mu=None, beta=None):
+        super().__init__()
+        self.mu = mu
+        self.beta = beta
+        self.name = "gumbel"
+        self.params = (self.mu, self.beta)
+        self.param_names = ("mu", "beta")
+        self.params_support = ((-np.inf, np.inf), (eps, np.inf))
+        self.dist = stats.gumbel_r
+        self.support = (-np.inf, np.inf)
+        self._update_rv_frozen()
+
+    def _get_frozen(self):
+        frozen = None
+        if any(self.params):
+            frozen = self.dist(loc=self.mu, scale=self.beta)
+        return frozen
+
+    def _update(self, mu, beta):
+        self.mu = mu
+        self.beta = beta
+        self.params = (self.mu, self.beta)
+        self._update_rv_frozen()
+
+    def _fit_moments(self, mean, sigma):
+        beta = sigma / np.pi * 6**0.5
+        mu = mean - beta * np.euler_gamma
+        self._update(mu, beta)
+
+    def _fit_mle(self, sample, **kwargs):
+        mu, beta = self.dist.fit(sample, **kwargs)
+        self._update(mu, beta)
+
+
 class HalfCauchy(Continuous):
     r"""
     HalfCauchy Distribution

preliz/tests/test_distributions.py

@@ -7,6 +7,7 @@
     Cauchy,
     ChiSquared,
     Gamma,
+    Gumbel,
     Exponential,
     HalfCauchy,
     HalfNormal,
@@ -38,6 +39,7 @@
         (Beta, (2, 5)),
         (ChiSquared, (1,)),
         (Gamma, (1, 0.5)),
+        (Gumbel, (1, 2)),
         (HalfNormal, (1,)),
         (HalfStudent, (3, 1)),
         (HalfStudent, (1000000, 1)),
@@ -88,6 +90,7 @@ def test_moments(distribution, params):
         (Cauchy, (0, 1)),
         (ChiSquared, (1,)),
         (Gamma, (1, 0.5)),
+        (Gumbel, (0, 1)),
         (HalfCauchy, (1,)),
         (HalfNormal, (1,)),
         (HalfStudent, (3, 1)),

preliz/tests/test_maxent.py

@@ -18,6 +18,7 @@
     ChiSquared,
     Exponential,
     Gamma,
+    Gumbel,
     Laplace,
     Logistic,
     LogNormal,
@@ -40,6 +41,7 @@
         (ChiSquared, "chisquared", 0, 4, 0.9, 1, (0, np.inf), (1.659)),
         (Exponential, "exponential", 0, 4, 0.9, None, (0, np.inf), (0.575)),
         (Gamma, "gamma", 0, 10, 0.7, None, (0, np.inf), (0.868, 0.103)),
+        (Gumbel, "gumbel", 0, 10, 0.9, None, (-np.inf, np.inf), (3.557, 2.598)),
         (HalfCauchy, "halfcauchy", 0, 10, 0.7, None, (0, np.inf), (5.095)),
         (HalfNormal, "halfnormal", 0, 10, 0.7, None, (0, np.inf), (9.648)),
         (HalfStudent, "halfstudent", 0, 10, 0.7, 3, (0, np.inf), (8.001)),

preliz/tests/test_mle.py

@@ -13,6 +13,7 @@
         (pz.ChiSquared, (1,)),
         (pz.Exponential, (5,)),
         (pz.Gamma, (2, 5)),
+        (pz.Gumbel, (0, 2)),
         (pz.HalfCauchy, (1,)),
         (pz.HalfNormal, (1,)),
         (pz.HalfStudent, (3, 1)),