feat: add new distributions: cauchy, beta, uniform and pareto I type

[iraedeus]

No description provided.

[Copilot]

Pull Request Overview

This PR adds four new statistical distribution models to the mpest framework: Cauchy, Beta, Uniform, and Pareto Type I distributions. Each implementation includes parameter transformation utilities, sampling methods, probability density function calculations, and derivative computations for optimization purposes.

• Full implementation of four new distribution models with both external and internal parameter representations
• Comprehensive test suites for each distribution covering parameter conversion, sampling, PDF computation, and derivative calculations
• Integration with the existing mpest model registry

Reviewed Changes

Copilot reviewed 9 out of 10 changed files in this pull request and generated 2 comments.

Show a summary per file

File	Description
mpest/models/uniform.py	Implements Uniform distribution with L-moments parameter estimation
mpest/models/pareto.py	Implements Pareto Type I distribution with log-transformed parameters
mpest/models/cauchy.py	Implements Cauchy distribution with log-scale parameterization
mpest/models/beta.py	Implements Beta distribution with log-transformed shape parameters
mpest/models/__init__.py	Registers the new distribution models in the framework
tests/models/test_uniform.py	Comprehensive test suite for Uniform distribution
tests/models/test_pareto.py	Comprehensive test suite for Pareto distribution
tests/models/test_cauchy.py	Comprehensive test suite for Cauchy distribution
tests/models/test_beta.py	Comprehensive test suite for Beta distribution

Comments suppressed due to low confidence (4)

tests/models/test_pareto.py:45

• [nitpick] The parameter name 'internal_params' is inconsistent with the function's purpose. Since this function tests converting FROM model parameters, the input should be named something like 'params' or 'model_params' to match the pattern used in other test files.

    def test_params_convert_from_model(self, internal_params):

tests/models/test_beta.py:113

• [nitpick] The parameter name 'param' is inconsistent with other test methods which use 'params'. This should be 'params' for consistency.

    def test_pdf(self, x, param):

mpest/models/uniform.py:46

• The method name 'lda' is ambiguous and unclear. Consider renaming to something more descriptive like 'ld_param_a' or 'derivative_wrt_a' to clearly indicate it's the derivative with respect to parameter 'a'.

    def lda(self, x: float, params: Params) -> float:

mpest/models/uniform.py:53

• The method name 'ldb' is ambiguous and unclear. Consider renaming to something more descriptive like 'ld_param_b' or 'derivative_wrt_b' to clearly indicate it's the derivative with respect to parameter 'b'.

    def ldb(self, x: float, params: Params) -> float: