Add efficient Moyal

docs/api_reference.rst

@@ -66,6 +66,9 @@ This reference provides detailed documentation for user functions in the current
 .. automodule:: preliz.distributions.lognormal
    :members:
 
+.. automodule:: preliz.distributions.moyal
+   :members:
+
 .. automodule:: preliz.distributions.normal
    :members:
 

preliz/distributions/continuous.py

@@ -30,6 +30,7 @@
 from .laplace import Laplace
 from .logistic import Logistic
 from .lognormal import LogNormal
+from .moyal import Moyal
 from .normal import Normal
 from .pareto import Pareto
 from .studentt import StudentT
@@ -443,86 +444,6 @@ def rvs(
         return expit(np.random.normal(self.mu, self.sigma, size))
 
 
-class Moyal(Continuous):
-    r"""
-    Moyal distribution.
-
-    The pdf of this distribution is
-
-    .. math::
-
-       f(x \mid \mu,\sigma) =
-            \frac{1}{\sqrt{2\pi}\sigma}e^{-\frac{1}{2}\left(z + e^{-z}\right)},
-
-    where
-
-    .. math::
-
-       z = \frac{x-\mu}{\sigma}
-
-    .. plot::
-        :context: close-figs
-
-        import arviz as az
-        from preliz import Moyal
-        az.style.use('arviz-doc')
-        mus = [-1., 0., 4.]
-        sigmas = [2., 1., 4.]
-        for mu, sigma in zip(mus, sigmas):
-            Moyal(mu, sigma).plot_pdf(support=(-10,20))
-
-    ========  ==============================================================
-    Support   :math:`x \in (-\infty, \infty)`
-    Mean      :math:`\mu + \sigma\left(\gamma + \log 2\right)`, where
-              :math:`\gamma` is the Euler-Mascheroni constant
-    Variance  :math:`\frac{\pi^{2}}{2}\sigma^{2}`
-    ========  ==============================================================
-
-    Parameters
-    ----------
-    mu : float
-        Location parameter.
-    sigma : float
-        Scale parameter (sigma > 0).
-    """
-
-    def __init__(self, mu=None, sigma=None):
-        super().__init__()
-        self.dist = copy(stats.moyal)
-        self.support = (-np.inf, np.inf)
-        self._parametrization(mu, sigma)
-
-    def _parametrization(self, mu=None, sigma=None):
-        self.mu = mu
-        self.sigma = sigma
-        self.params = (self.mu, self.sigma)
-        self.param_names = ("mu", "sigma")
-        self.params_support = ((-np.inf, np.inf), (eps, np.inf))
-        if all_not_none(mu, sigma):
-            self._update(self.mu, self.sigma)
-
-    def _get_frozen(self):
-        frozen = None
-        if all_not_none(self.params):
-            frozen = self.dist(loc=self.mu, scale=self.sigma)
-        return frozen
-
-    def _update(self, mu, sigma):
-        self.mu = np.float64(mu)
-        self.sigma = np.float64(sigma)
-        self.params = (self.mu, self.sigma)
-        self._update_rv_frozen()
-
-    def _fit_moments(self, mean, sigma):
-        sigma = sigma / np.pi * 2**0.5
-        mu = mean - sigma * (np.euler_gamma + np.log(2))
-        self._update(mu, sigma)
-
-    def _fit_mle(self, sample, **kwargs):
-        mu, sigma = self.dist.fit(sample, **kwargs)
-        self._update(mu, sigma)
-
-
 class Rice(Continuous):
     r"""
     Rice distribution.

preliz/distributions/moyal.py

@@ -0,0 +1,170 @@
+# pylint: disable=attribute-defined-outside-init
+# pylint: disable=arguments-differ
+import numba as nb
+import numpy as np
+from scipy.special import erf, erfinv, zeta  # pylint: disable=no-name-in-module
+
+from .distributions import Continuous
+from ..internal.distribution_helper import eps, all_not_none
+from ..internal.special import erf, erfinv, ppf_bounds_cont
+from ..internal.optimization import optimize_ml
+
+
+class Moyal(Continuous):
+    r"""
+    Moyal distribution.
+
+    The pdf of this distribution is
+
+    .. math::
+
+       f(x \mid \mu,\sigma) =
+            \frac{1}{\sqrt{2\pi}\sigma}e^{-\frac{1}{2}\left(z + e^{-z}\right)},
+
+    where
+
+    .. math::
+
+       z = \frac{x-\mu}{\sigma}
+
+    .. plot::
+        :context: close-figs
+
+        import arviz as az
+        from preliz import Moyal
+        az.style.use('arviz-doc')
+        mus = [-1., 0., 4.]
+        sigmas = [2., 1., 4.]
+        for mu, sigma in zip(mus, sigmas):
+            Moyal(mu, sigma).plot_pdf(support=(-10,20))
+
+    ========  ==============================================================
+    Support   :math:`x \in (-\infty, \infty)`
+    Mean      :math:`\mu + \sigma\left(\gamma + \log 2\right)`, where
+              :math:`\gamma` is the Euler-Mascheroni constant
+    Variance  :math:`\frac{\pi^{2}}{2}\sigma^{2}`
+    ========  ==============================================================
+
+    Parameters
+    ----------
+    mu : float
+        Location parameter.
+    sigma : float
+        Scale parameter (sigma > 0).
+    """
+
+    def __init__(self, mu=None, sigma=None):
+        super().__init__()
+        self.support = (-np.inf, np.inf)
+        self._parametrization(mu, sigma)
+
+    def _parametrization(self, mu=None, sigma=None):
+        self.mu = mu
+        self.sigma = sigma
+        self.params = (self.mu, self.sigma)
+        self.param_names = ("mu", "sigma")
+        self.params_support = ((-np.inf, np.inf), (eps, np.inf))
+        if all_not_none(mu, sigma):
+            self._update(self.mu, self.sigma)
+
+    def _update(self, mu, sigma):
+        self.mu = np.float64(mu)
+        self.sigma = np.float64(sigma)
+        self.params = (self.mu, self.sigma)
+        self.is_frozen = True
+
+    def pdf(self, x):
+        """
+        Compute the probability density function (PDF) at a given point x.
+        """
+        x = np.asarray(x)
+        return np.exp(self.logpdf(x))
+
+    def cdf(self, x):
+        """
+        Compute the cumulative distribution function (CDF) at a given point x.
+        """
+        x = np.asarray(x)
+        return nb_cdf(x, self.mu, self.sigma)
+
+    def ppf(self, q):
+        """
+        Compute the percent point function (PPF) at a given probability q.
+        """
+        q = np.asarray(q)
+        return nb_ppf(q, self.mu, self.sigma)
+
+    def logpdf(self, x):
+        """
+        Compute the log probability density function (log PDF) at a given point x.
+        """
+        return nb_logpdf(x, self.mu, self.sigma)
+
+    def _neg_logpdf(self, x):
+        """
+        Compute the neg log_pdf sum for the array x.
+        """
+        return nb_neg_logpdf(x, self.mu, self.sigma)
+
+    def entropy(self):
+        x_values = self.xvals("restricted")
+        logpdf = self.logpdf(x_values)
+        return -np.trapz(np.exp(logpdf) * logpdf, x_values)
+
+    def mean(self):
+        return self.mu + self.sigma * (np.euler_gamma + np.log(2))
+
+    def median(self):
+        return self.ppf(0.5)
+
+    def var(self):
+        return self.sigma**2 * (np.pi**2) / 2
+
+    def std(self):
+        return self.var() ** 0.5
+
+    def skewness(self):
+        return 28 * np.sqrt(2) * zeta(3) / np.pi**3
+
+    def kurtosis(self):
+        return 4
+
+    def rvs(self, size=None, random_state=None):
+        random_state = np.random.default_rng(random_state)
+        return self.ppf(random_state.random(size))
+
+    def _fit_moments(self, mean, sigma):
+        sigma = sigma / np.pi * 2**0.5
+        mu = mean - sigma * (np.euler_gamma + np.log(2))
+        self._update(mu, sigma)
+
+    def _fit_mle(self, sample):
+        optimize_ml(self, sample)
+
+
+@nb.njit(cache=True)
+def nb_cdf(x, mu, sigma):
+    z_val = (x - mu) / sigma
+    return 1 - erf(np.exp(-z_val / 2) * (2**-0.5))
+
+
+@nb.njit(cache=True)
+def nb_ppf(q, mu, sigma):
+    x_val = sigma * -np.log(2.0 * erfinv(1 - q) ** 2) + mu
+    return ppf_bounds_cont(x_val, q, -np.inf, np.inf)
+
+
+@nb.njit(cache=True)
+def nb_entropy(sigma):
+    return 0.5 * (np.log(2 * np.pi * np.e * sigma**2))
+
+
+@nb.njit(cache=True)
+def nb_logpdf(x, mu, sigma):
+    z_val = (x - mu) / sigma
+    return -(1 / 2) * (z_val + np.exp(-z_val)) - np.log(sigma) - (1 / 2) * np.log(2 * np.pi)
+
+
+@nb.njit(cache=True)
+def nb_neg_logpdf(x, mu, sigma):
+    return -(nb_logpdf(x, mu, sigma)).sum()

preliz/tests/test_scipy.py

@@ -20,6 +20,7 @@
     Laplace,
     Logistic,
     LogNormal,
+    Moyal,
     Normal,
     Pareto,
     StudentT,
@@ -66,6 +67,7 @@
         (Laplace, stats.laplace, {"mu": 2.5, "b": 4}, {"loc": 2.5, "scale": 4}),
         (Logistic, stats.logistic, {"mu": 2.5, "s": 4}, {"loc": 2.5, "scale": 4}),
         (LogNormal, stats.lognorm, {"mu": 0, "sigma": 2}, {"s": 2, "scale": 1}),
+        (Moyal, stats.moyal, {"mu": 1, "sigma": 2}, {"loc": 1, "scale": 2}),
         (Normal, stats.norm, {"mu": 0, "sigma": 2}, {"loc": 0, "scale": 2}),
         (Pareto, stats.pareto, {"m": 1, "alpha": 4.5}, {"b": 4.5}),
         (StudentT, stats.t, {"nu": 5, "mu": 0, "sigma": 2}, {"df": 5, "loc": 0, "scale": 2}),
@@ -122,7 +124,7 @@ def test_match_scipy(p_dist, sp_dist, p_params, sp_params):
         expected = scipy_dist.entropy()
         if preliz_dist.kind == "discrete":
             assert_almost_equal(actual, expected, decimal=1)
-        elif preliz_name == "HalfStudentT":
+        elif preliz_name in ["HalfStudentT", "Moyal"]:
             assert_almost_equal(actual, expected, decimal=2)
         else:
             assert_almost_equal(actual, expected, decimal=4)
@@ -134,6 +136,7 @@ def test_match_scipy(p_dist, sp_dist, p_params, sp_params):
     if preliz_name in [
         "HalfStudentT",
         "Kumaraswamy",
+        "Moyal",
         "StudentT",
         "Weibull",
         "InverseGamma",