Add generalized gamma distribution functions and loglogistic log cdfs

[yananlong]

Summary

• add loglogistic_lcdf and loglogistic_lccdf implementations with analytic gradients
• implement generalized_gamma lpdf/lcdf/lccdf/rng following the Prentice parameterization and expose them through prim/prob.hpp
• add unit tests covering loglogistic log CDFs and generalized gamma special cases, including RNG behavior

Testing

• ./runTests.py test/unit/math/prim/prob/loglogistic_lcdf_lccdf_test.cpp
• ./runTests.py test/unit/math/prim/prob/generalized_gamma_special_cases_test.cpp

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https://chatgpt.com/codex/tasks/task_b_68e6664bfbac8320abd0c40838d2c304

[Copilot]

Pull Request Overview

This PR adds log CDF functions for the loglogistic distribution and implements the generalized gamma distribution following the Prentice parameterization.

• Implements loglogistic_lcdf and loglogistic_lccdf functions with analytic gradients
• Adds a complete generalized gamma distribution implementation including lpdf, lcdf, lccdf, and rng functions
• Includes comprehensive unit tests verifying the new functions and special case reductions

Reviewed Changes

Copilot reviewed 9 out of 9 changed files in this pull request and generated no comments.

Show a summary per file

File	Description
test/unit/math/prim/prob/loglogistic_lcdf_lccdf_test.cpp	Unit tests for loglogistic log CDF functions
test/unit/math/prim/prob/generalized_gamma_special_cases_test.cpp	Unit tests for generalized gamma special case reductions
stan/math/prim/prob/loglogistic_lcdf.hpp	Implementation of loglogistic log CDF
stan/math/prim/prob/loglogistic_lccdf.hpp	Implementation of loglogistic log complementary CDF
stan/math/prim/prob/generalized_gamma_rng.hpp	Random number generation for generalized gamma
stan/math/prim/prob/generalized_gamma_lpdf.hpp	Log PDF implementation for generalized gamma
stan/math/prim/prob/generalized_gamma_lcdf.hpp	Log CDF implementation for generalized gamma
stan/math/prim/prob/generalized_gamma_lccdf.hpp	Log complementary CDF for generalized gamma
stan/math/prim/prob.hpp	Header file updates to expose new functions

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[Copilot]

Pull Request Overview

Copilot reviewed 9 out of 9 changed files in this pull request and generated 1 comment.

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