feat(families): add uniform distribution family

- Implement Uniform distribution family with multiple parameterizations:
  * standard (a, b) - base parametrization with constraint a < b
  * meanWidth (m, r) - center-radius parametrization
  * minRange (minimum, range) - [minimum, minimum+range] parametrization
- Add all analytical characteristics: PDF, CDF, PPF, characteristic function, moments
- Implement proper support calculation for uniform distribution [a, b]
- Register family in ParametricFamilyRegister
- Families' naming style changed from 'typefamily family' to 'typefamily'

Author: TheodorDM

src/pysatl_core/families/configuration.py

@@ -5,6 +5,7 @@
 This module defines and configures parametric distribution families for the PySATL library:
 
 - :class:`Normal Family` — Gaussian distribution with multiple parameterizations.
+- :class:`Uniform Family` — Gaussian distribution with multiple parameterizations.
 
 Notes
 -----
@@ -69,6 +70,7 @@ def configure_families_register() -> ParametricFamilyRegister:
         The global registry of parametric families.
     """
     _configure_normal_family()
+    _configure_uniform_family()
     return ParametricFamilyRegister()
 
 
@@ -323,7 +325,7 @@ def skew_func(_1: Parametrization, _2: Any) -> int:
         return 0
 
     def kurt_func(_1: Parametrization, _2: Any, excess: bool = False) -> int:
-        """Raw or excess kurtosis of normal distribution (always 3).
+        """Raw or excess kurtosis of normal distribution.
 
         Parameters
         ----------
@@ -344,10 +346,11 @@ def kurt_func(_1: Parametrization, _2: Any, excess: bool = False) -> int:
             return 0
 
     def _normal_support(_: Parametrization) -> ContinuousSupport:
+        """Support of normal distribution"""
         return ContinuousSupport()
 
     Normal = ParametricFamily(
-        name="Normal Family",
+        name="Normal",
         distr_type=UnivariateContinuous,
         distr_parametrizations=["meanStd", "meanPrec", "exponential"],
         distr_characteristics={
@@ -372,6 +375,332 @@ def _normal_support(_: Parametrization) -> ContinuousSupport:
     ParametricFamilyRegister.register(Normal)
 
 
+@dataclass
+class UniformStandardParametrization(Parametrization):
+    """
+    Standard parametrization of uniform distribution.
+
+    Parameters
+    ----------
+    lower_bound : float
+        Lower bound of the distribution
+    upper_bound : float
+        Upper bound of the distribution
+    """
+
+    lower_bound: float
+    upper_bound: float
+
+    @constraint(description="lower_bound < upper_bound")
+    def check_lower_less_than_upper(self) -> bool:
+        """Check that lower bound is less than upper bound."""
+        return self.lower_bound < self.upper_bound
+
+
+@dataclass
+class UniformMeanWidthParametrization(Parametrization):
+    """
+    Mean-width parametrization of uniform distribution.
+
+    Parameters
+    ----------
+    mean : float
+        Mean (center) of the distribution
+    width : float
+        Width of the distribution (upper_bound - lower_bound)
+    """
+
+    mean: float
+    width: float
+
+    @constraint(description="width > 0")
+    def check_width_positive(self) -> bool:
+        """Check that width is positive."""
+        return self.width > 0
+
+    def transform_to_base_parametrization(self) -> Parametrization:
+        """
+        Transform to Standard parametrization.
+
+        Returns
+        -------
+        Parametrization
+            Standard parametrization instance
+        """
+        half_width = self.width / 2
+        return UniformStandardParametrization(
+            lower_bound=self.mean - half_width, upper_bound=self.mean + half_width
+        )
+
+
+@dataclass
+class UniformMinRangeParametrization(Parametrization):
+    """
+    Minimum-range parametrization of uniform distribution.
+
+    Parameters
+    ----------
+    minimum : float
+        Minimum value (lower bound)
+    range_val : float
+        Range of the distribution (upper_bound - lower_bound)
+    """
+
+    minimum: float
+    range_val: float
+
+    @constraint(description="range_val > 0")
+    def check_range_positive(self) -> bool:
+        """Check that range is positive."""
+        return self.range_val > 0
+
+    def transform_to_base_parametrization(self) -> Parametrization:
+        """
+        Transform to Standard parametrization.
+
+        Returns
+        -------
+        Parametrization
+            Standard parametrization instance
+        """
+        return UniformStandardParametrization(
+            lower_bound=self.minimum, upper_bound=self.minimum + self.range_val
+        )
+
+
+def _configure_uniform_family() -> None:
+    UNIFORM_DOC = """
+    Uniform (continuous) distribution.
+
+    The uniform distribution is a continuous probability distribution where
+    all intervals of the same length are equally probable. It is defined by
+    two parameters: lower bound and upper bound.
+
+    Probability density function:
+        f(x) = 1/(upper_bound - lower_bound) for x in [lower_bound, upper_bound], 0 otherwise
+
+    The uniform distribution is often used when there is no prior knowledge
+    about the possible values of a variable, representing maximum uncertainty.
+    """
+
+    def uniform_pdf(
+        parameters: Parametrization, x: npt.NDArray[np.float64]
+    ) -> npt.NDArray[np.float64]:
+        """
+        Probability density function for uniform distribution.
+        Uses np.clip for vectorized computation:
+            - For x < lower_bound: returns 0
+            - For x > upper_bound: returns 1
+            - Otherwise: returns (x - lower_bound) / (upper_bound - lower_bound)
+
+        Parameters
+        ----------
+        parameters : Parametrization
+            Distribution parameters object with fields:
+            - lower_bound: float (lower bound)
+            - upper_bound: float (upper bound)
+        x : npt.NDArray[np.float64]
+            Points at which to evaluate the probability density function
+
+        Returns
+        -------
+        npt.NDArray[np.float64]
+            Probability density values at points x
+        """
+        parameters = cast(UniformStandardParametrization, parameters)
+
+        lower_bound = parameters.lower_bound
+        upper_bound = parameters.upper_bound
+
+        return np.where(
+            (x >= lower_bound) & (x <= upper_bound), 1.0 / (upper_bound - lower_bound), 0.0
+        )
+
+    def uniform_cdf(
+        parameters: Parametrization, x: npt.NDArray[np.float64]
+    ) -> npt.NDArray[np.float64]:
+        """
+        Cumulative distribution function for uniform distribution.
+        Uses np.clip for vectorized computation:
+            - For x < lower_bound: returns 0
+            - For x > upper_bound: returns 1
+
+        Parameters
+        ----------
+        parameters : Parametrization
+            Distribution parameters object with fields:
+            - lower_bound: float (lower bound)
+            - upper_bound: float (upper bound)
+        x : npt.NDArray[np.float64]
+            Points at which to evaluate the cumulative distribution function
+
+        Returns
+        -------
+        npt.NDArray[np.float64]
+            Probabilities P(X ≤ x) for each point x
+        """
+        parameters = cast(UniformStandardParametrization, parameters)
+
+        lower_bound = parameters.lower_bound
+        upper_bound = parameters.upper_bound
+
+        return np.clip((x - lower_bound) / (upper_bound - lower_bound), 0.0, 1.0)
+
+    def uniform_ppf(
+        parameters: Parametrization, p: npt.NDArray[np.float64]
+    ) -> npt.NDArray[np.float64]:
+        """
+        Percent point function (inverse CDF) for uniform distribution.
+
+        For uniform distribution on [lower_bound, upper_bound]:
+        - For p = 0: returns lower_bound
+        - For p = 1: returns upper_bound
+        - For p in (0, 1): returns lower_bound + p × (upper_bound - lower_bound)
+
+        Parameters
+        ----------
+        parameters : Parametrization
+            Distribution parameters object with fields:
+            - lower_bound: float (lower bound)
+            - upper_bound: float (upper bound)
+        p : npt.NDArray[np.float64]
+            Probability from [0, 1]
+
+        Returns
+        -------
+        npt.NDArray[np.float64]
+            Quantiles corresponding to probabilities p
+
+        Raises
+        ------
+        ValueError
+            If probability is outside [0, 1]
+        """
+        if np.any((p < 0) | (p > 1)):
+            raise ValueError("Probability must be in [0, 1]")
+
+        parameters = cast(UniformStandardParametrization, parameters)
+        lower_bound = parameters.lower_bound
+        upper_bound = parameters.upper_bound
+
+        return cast(npt.NDArray[np.float64], lower_bound + p * (upper_bound - lower_bound))
+
+    def uniform_char_func(
+        parameters: Parametrization, t: npt.NDArray[np.float64]
+    ) -> npt.NDArray[np.complex128]:
+        """
+        Characteristic function of uniform distribution.
+
+        Characteristic function formula for uniform distribution on [lower_bound, upper bound]:
+            φ(t) = sinc((upper bound - lower_bound) * t / 2) *
+            * exp(i * (lower_bound + upper bound) * t / 2)
+        where sinc(x) = sin(πx)/(πx) as defined by numpy.
+
+        Parameters
+        ----------
+        parameters : Parametrization
+            Distribution parameters object with fields:
+            - lower_bound: float (lower bound)
+            - upper_bound: float (upper bound)
+        t : npt.NDArray[np.float64]
+            Points at which to evaluate the characteristic function
+
+        Returns
+        -------
+        npt.NDArray[np.complex128]
+            Characteristic function values at points t
+        """
+        parameters = cast(UniformStandardParametrization, parameters)
+
+        lower_bound = parameters.lower_bound
+        upper_bound = parameters.upper_bound
+
+        width = upper_bound - lower_bound
+        center = (lower_bound + upper_bound) / 2
+
+        t_arr = np.asarray(t, dtype=np.float64)
+
+        x = width * t_arr / (2 * np.pi)
+        sinc_val = np.sinc(x)
+
+        return cast(npt.NDArray[np.complex128], sinc_val * np.exp(1j * center * t_arr))
+
+    def mean_func(parameters: Parametrization, _: Any) -> float:
+        """Mean of uniform distribution."""
+        parameters = cast(UniformStandardParametrization, parameters)
+        return (parameters.lower_bound + parameters.upper_bound) / 2
+
+    def var_func(parameters: Parametrization, _: Any) -> float:
+        """Variance of uniform distribution."""
+        parameters = cast(UniformStandardParametrization, parameters)
+        width = parameters.upper_bound - parameters.lower_bound
+        return width**2 / 12
+
+    def skew_func(_1: Parametrization, _2: Any) -> int:
+        """Skewness of uniform distribution (always 0)."""
+        return 0
+
+    def kurt_func(_1: Parametrization, _2: Any, excess: bool = False) -> float:
+        """Raw or excess kurtosis of uniform distribution.
+
+        Parameters
+        ----------
+        _1 : Parametrization
+            Needed by architecture parameter
+        _2 : Any
+            Needed by architecture parameter
+        excess : bool
+            A value defines if there will be raw or excess kurtosis
+            default is False
+
+        Returns
+        -------
+        float
+            Kurtosis value
+        """
+        if not excess:
+            return 1.8
+        else:
+            return -1.2
+
+    def _uniform_support(parameters: Parametrization) -> ContinuousSupport:
+        """Support of uniform distribution"""
+        parameters = cast(
+            UniformStandardParametrization, parameters.transform_to_base_parametrization()
+        )
+        return ContinuousSupport(
+            left=parameters.lower_bound,
+            right=parameters.upper_bound,
+            left_closed=True,
+            right_closed=True,
+        )
+
+    Uniform = ParametricFamily(
+        name="ContinuousUniform",
+        distr_type=UnivariateContinuous,
+        distr_parametrizations=["standard", "meanWidth", "minRange"],
+        distr_characteristics={
+            PDF: uniform_pdf,
+            CDF: uniform_cdf,
+            PPF: uniform_ppf,
+            CF: uniform_char_func,
+            MEAN: mean_func,
+            VAR: var_func,
+            SKEW: skew_func,
+            KURT: kurt_func,
+        },
+        sampling_strategy=DefaultSamplingUnivariateStrategy(),
+        support_by_parametrization=_uniform_support,
+    )
+    Uniform.__doc__ = UNIFORM_DOC
+
+    parametrization(family=Uniform, name="standard")(UniformStandardParametrization)
+    parametrization(family=Uniform, name="meanWidth")(UniformMeanWidthParametrization)
+    parametrization(family=Uniform, name="minRange")(UniformMinRangeParametrization)
+
+    ParametricFamilyRegister.register(Uniform)
+
+
 def reset_families_register() -> None:
     configure_families_register.cache_clear()
     ParametricFamilyRegister._reset()