test(families): tests for exponential family

Author: MyznikovFD

tests/unit/families/builtins/continuous/test_exponential.py

@@ -0,0 +1,261 @@
+"""
+Tests for Exponential Distribution Family
+
+This module tests the functionality of the exponential distribution family,
+including parameterizations, characteristics, and sampling.
+"""
+
+__author__ = "Fedor Myznikov"
+__copyright__ = "Copyright (c) 2025 PySATL project"
+__license__ = "SPDX-License-Identifier: MIT"
+
+
+import numpy as np
+import pytest
+from scipy.stats import expon
+
+from pysatl_core.distributions.support import ContinuousSupport
+from pysatl_core.families.configuration import configure_families_register
+from pysatl_core.types import (
+    CharacteristicName,
+    ContinuousSupportShape1D,
+    FamilyName,
+    UnivariateContinuous,
+)
+
+from .base import BaseDistributionTest
+
+
+class TestExponentialFamily(BaseDistributionTest):
+    """Test suite for Exponential distribution family."""
+
+    def setup_method(self):
+        """Setup before each test method."""
+        registry = configure_families_register()
+        self.exponential_family = registry.get(FamilyName.EXPONENTIAL)
+        self.exponential_dist_example = self.exponential_family(lambda_=0.5)
+
+    def test_family_properties(self):
+        """Test basic properties of exponential family."""
+        assert self.exponential_family.name == FamilyName.EXPONENTIAL
+
+        # Check parameterizations
+        expected_parametrizations = {"rate", "scale"}
+        assert set(self.exponential_family.parametrization_names) == expected_parametrizations
+        assert self.exponential_family.base_parametrization_name == "rate"
+
+    def test_rate_parametrization_creation(self):
+        """Test creation of distribution with rate parametrization."""
+        dist = self.exponential_family(lambda_=0.5)
+
+        assert dist.family_name == FamilyName.EXPONENTIAL
+        assert dist.distribution_type == UnivariateContinuous
+        assert dist.parameters == {"lambda_": 0.5}
+        assert dist.parametrization_name == "rate"
+
+    def test_scale_parametrization_creation(self):
+        """Test creation of distribution with scale parametrization."""
+        dist = self.exponential_family(beta=2.0, parametrization_name="scale")
+
+        assert dist.parameters == {"beta": 2.0}
+        assert dist.parametrization_name == "scale"
+
+    def test_parametrization_constraints(self):
+        """Test parameter constraints validation."""
+        # lambda_ must be positive
+        with pytest.raises(ValueError, match="lambda_ > 0"):
+            self.exponential_family(lambda_=-1.0)
+
+        # beta must be positive
+        with pytest.raises(ValueError, match="beta > 0"):
+            self.exponential_family(beta=0.0, parametrization_name="scale")
+
+    def test_moments(self):
+        """Test moment calculations."""
+        # Mean
+        mean_func = self.exponential_dist_example.query_method(CharacteristicName.MEAN)
+        assert abs(mean_func(None) - 2.0) < self.CALCULATION_PRECISION
+
+        # Variance
+        var_func = self.exponential_dist_example.query_method(CharacteristicName.VAR)
+        assert abs(var_func(None) - 4.0) < self.CALCULATION_PRECISION
+
+        # Skewness
+        skew_func = self.exponential_dist_example.query_method(CharacteristicName.SKEW)
+        assert abs(skew_func(None) - 2.0) < self.CALCULATION_PRECISION
+
+    def test_kurtosis_calculation(self):
+        """Test kurtosis calculation with excess parameter."""
+        kurt_func = self.exponential_dist_example.query_method(CharacteristicName.KURT)
+
+        raw_kurt = kurt_func(None)
+        assert abs(raw_kurt - 9.0) < self.CALCULATION_PRECISION
+
+        excess_kurt = kurt_func(None, excess=True)
+        assert abs(excess_kurt - 6.0) < self.CALCULATION_PRECISION
+
+        raw_kurt_explicit = kurt_func(None, excess=False)
+        assert abs(raw_kurt_explicit - 9.0) < self.CALCULATION_PRECISION
+
+    @pytest.mark.parametrize(
+        "parametrization_name, params, expected_lambda",
+        [
+            ("rate", {"lambda_": 0.5}, 0.5),
+            ("scale", {"beta": 2.0}, 0.5),  # lambda = 1/beta = 0.5
+        ],
+    )
+    def test_parametrization_conversions(self, parametrization_name, params, expected_lambda):
+        """Test conversions between different parameterizations."""
+        base_params = self.exponential_family.to_base(
+            self.exponential_family.get_parametrization(parametrization_name)(**params)
+        )
+
+        assert abs(base_params.parameters["lambda_"] - expected_lambda) < self.CALCULATION_PRECISION
+
+    def test_analytical_computations_availability(self):
+        """Test that analytical computations are available for exponential distribution."""
+        comp = self.exponential_family(lambda_=1.0).analytical_computations
+
+        expected_chars = {
+            CharacteristicName.PDF,
+            CharacteristicName.CDF,
+            CharacteristicName.PPF,
+            CharacteristicName.CF,
+            CharacteristicName.MEAN,
+            CharacteristicName.VAR,
+            CharacteristicName.SKEW,
+            CharacteristicName.KURT,
+        }
+        assert set(comp.keys()) == expected_chars
+
+    def test_pdf_array_input(self):
+        """Test PDF calculation with array input."""
+        pdf = self.exponential_dist_example.query_method(CharacteristicName.PDF)
+        x_array = np.array([-1.0, 0.0, 1.0, 2.0, 3.0, 4.0])
+
+        pdf_array = pdf(x_array)
+        assert pdf_array.shape == x_array.shape
+        scipy_pdf = expon.pdf(x_array, scale=2.0)  # scale = 1/lambda = 2.0
+
+        self.assert_arrays_almost_equal(pdf_array, scipy_pdf)
+
+    def test_cdf_array_input(self):
+        """Test CDF calculation with array input."""
+        cdf = self.exponential_dist_example.query_method(CharacteristicName.CDF)
+        x_array = np.array([-1.0, 0.0, 1.0, 2.0, 3.0, 4.0])
+
+        cdf_array = cdf(x_array)
+        assert cdf_array.shape == x_array.shape
+        scipy_cdf = expon.cdf(x_array, scale=2.0)  # scale = 1/lambda = 2.0
+
+        self.assert_arrays_almost_equal(cdf_array, scipy_cdf)
+
+    def test_ppf_array_input(self):
+        """Test PPF calculation with array input."""
+        ppf = self.exponential_dist_example.query_method(CharacteristicName.PPF)
+        p_array = np.array([0.001, 0.01, 0.1, 0.25, 0.5, 0.75, 0.9, 0.99, 0.999])
+
+        ppf_array = ppf(p_array)
+        assert ppf_array.shape == p_array.shape
+        scipy_ppf = expon.ppf(p_array, scale=2.0)  # scale = 1/lambda = 2.0
+
+        self.assert_arrays_almost_equal(ppf_array, scipy_ppf)
+
+    def test_characteristic_function_array_input(self):
+        """Test characteristic function calculation with array input."""
+        char_func = self.exponential_dist_example.query_method(CharacteristicName.CF)
+        t_array = np.array([-2.0, -1.0, 0.0, 1.0, 2.0])
+
+        cf_array = char_func(t_array)
+        assert cf_array.shape == t_array.shape
+
+        lambda_ = 0.5
+        denominator = lambda_**2 + t_array**2
+        expected_real = lambda_**2 / denominator
+        expected_imag = lambda_ * t_array / denominator
+
+        expected_real = np.where(np.abs(t_array) < self.CALCULATION_PRECISION, 1.0, expected_real)
+        expected_imag = np.where(np.abs(t_array) < self.CALCULATION_PRECISION, 0.0, expected_imag)
+
+        expected = expected_real + 1j * expected_imag
+
+        self.assert_arrays_almost_equal(cf_array.real, expected.real)
+        self.assert_arrays_almost_equal(cf_array.imag, expected.imag)
+
+    def test_exponential_support(self):
+        """Test that exponential distribution has correct support [0, ∞)."""
+        dist = self.exponential_dist_example
+
+        assert dist.support is not None
+        assert isinstance(dist.support, ContinuousSupport)
+
+        assert dist.support.left == 0.0
+        assert dist.support.right == float("inf")
+        assert dist.support.left_closed
+        assert not dist.support.right_closed
+
+        # Test containment
+        assert dist.support.contains(0.0) is True
+        assert dist.support.contains(1.0) is True
+        assert dist.support.contains(-0.1) is False
+        assert dist.support.contains(float("inf")) is False
+
+        # Test array
+        test_points = np.array([-0.1, 0.0, 1.0, 10.0])
+        expected = np.array([False, True, True, True])
+        results = dist.support.contains(test_points)
+        np.testing.assert_array_equal(results, expected)
+
+        assert dist.support.shape == ContinuousSupportShape1D.RAY_RIGHT
+
+
+class TestExponentialFamilyEdgeCases(BaseDistributionTest):
+    """Test edge cases and error conditions for exponential distribution."""
+
+    def setup_method(self):
+        """Setup before each test method."""
+        registry = configure_families_register()
+        self.exponential_family = registry.get(FamilyName.EXPONENTIAL)
+
+    def test_invalid_parameterization(self):
+        """Test error for invalid parameterization name."""
+        with pytest.raises(KeyError):
+            self.exponential_family.distribution(parametrization_name="invalid_name", lambda_=1.0)
+
+    def test_missing_parameters(self):
+        """Test error for missing required parameters."""
+        with pytest.raises(TypeError):
+            self.exponential_family.distribution()  # Missing lambda_
+
+    def test_invalid_probability_ppf(self):
+        """Test PPF with invalid probability values."""
+        dist = self.exponential_family(lambda_=1.0)
+        ppf = dist.query_method(CharacteristicName.PPF)
+
+        # Test boundaries
+        assert ppf(0.0) == 0.0
+        assert ppf(1.0) == float("inf")
+
+        # Test invalid probabilities
+        with pytest.raises(ValueError):
+            ppf(-0.1)
+        with pytest.raises(ValueError):
+            ppf(1.1)
+
+    def test_characteristic_function_at_zero(self):
+        """Test characteristic function at zero returns 1."""
+        dist = self.exponential_family(lambda_=1.0)
+        char_func = dist.query_method(CharacteristicName.CF)
+
+        cf_value_zero = char_func(0.0)
+        assert abs(cf_value_zero.real - 1.0) < self.CALCULATION_PRECISION
+        assert abs(cf_value_zero.imag) < self.CALCULATION_PRECISION
+
+    def test_characteristic_function_large_t(self):
+        """Test characteristic function with large t."""
+        dist = self.exponential_family(lambda_=1.0)
+        char_func = dist.query_method(CharacteristicName.CF)
+
+        cf_value_large = char_func(1000.0)
+        assert np.iscomplexobj(cf_value_large)
+        assert abs(cf_value_large) <= 1.0