feat: implement betaincinv function

[devesssi]

Resolves #649

Description

What is the purpose of this pull request?

This pull request:

• Implements the inverse incomplete beta function (betaincinv) as a native Node.js addon
• Provides a JavaScript wrapper with input validation and error handling
• Includes comprehensive test suite, examples, and benchmarks
• Adds documentation with usage examples and parameter descriptions

The implementation uses the Newton-Raphson method to find the inverse of the incomplete beta function, which is useful in various statistical applications including hypothesis testing and confidence interval calculations.

Related Issues

Does this pull request have any related issues?

This pull request:

• Resolves [RFC]: Add C implementations to base special math functions (tracking issue) #649 by implementing the inverse incomplete beta function

Questions

Any questions for reviewers of this pull request?

No.

Other

Any other information relevant to this pull request?

Implementation Details:

• Uses Newton-Raphson method for finding the inverse
• Implements the incomplete beta function using continued fraction expansion
• Handles edge cases and invalid inputs
• Includes proper error handling and input validation

Technical Requirements:

• Node.js >=14.0.0 <19.0.0
• Uses node-addon-api for native module binding
• No breaking changes
  

Checklist

Please ensure the following tasks are completed before submitting this pull request.

• Read, understood, and followed the contributing guidelines
• Added comprehensive test suite
• Added examples and benchmarks
• Added documentation with usage examples
• Implemented proper error handling
• Added input validation
• Used consistent code style
• Added appropriate license headers
• Added proper type definitions
• Added proper JSDoc comments

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