[RFC]: Tracking issue for complete implementation of `@stdlib/stats/base/dists/halfnormal` package

[navyansh007]

Description

This tracking issue proposes adding comprehensive support for the half-normal distribution in @stdlib/stats/base/dists/halfnormal. The half-normal distribution is the distribution of the absolute value of a normally distributed random variable with mean 0. It is commonly used in statistical applications such as stochastic frontier analysis, modeling measurement errors, and other fields where only the magnitude of a normally distributed variable is of interest.

Rationale

Why is this feature important?

1. Completeness: Expanding stdlib's statistical distributions library to include the half-normal distribution provides users with a comprehensive set of tools for statistical analysis.

2. Common Use Cases: The half-normal distribution is widely used in:

   • Stochastic frontier analysis
   • Quality control and process capability studies
   • Modeling absolute deviations and measurement errors
   • Bayesian analysis as a prior distribution

3. Consistency: Following stdlib's existing patterns for probability distributions ensures a consistent API and user experience.

4. Scientific Computing: Enables researchers and data scientists to perform half-normal distribution calculations natively within stdlib without external dependencies.

Proposed Solution

How do you propose to implement this feature?

Implement the half-normal distribution following the established pattern used for other continuous distributions in stdlib (e.g., normal, exponential, gamma). This includes creating subpackages for various distribution functions, properties, and utilities within @stdlib/stats/base/dists/halfnormal/.

Implementation Checklist

The following subpackages need to be implemented for the half-normal distribution:

Core Distribution Functions

• @stdlib/stats/base/dists/halfnormal/cdf - Cumulative distribution function (CDF)
• @stdlib/stats/base/dists/halfnormal/pdf - Probability density function (PDF)
• @stdlib/stats/base/dists/halfnormal/quantile - Quantile function (inverse CDF)
• @stdlib/stats/base/dists/halfnormal/logcdf - Logarithm of cumulative distribution function
• @stdlib/stats/base/dists/halfnormal/logpdf - Logarithm of probability density function

Distribution Properties

• @stdlib/stats/base/dists/halfnormal/mean - Expected value (mean)
• @stdlib/stats/base/dists/halfnormal/median - Median
• @stdlib/stats/base/dists/halfnormal/mode - Mode
• @stdlib/stats/base/dists/halfnormal/variance - Variance
• @stdlib/stats/base/dists/halfnormal/stdev - Standard deviation
• @stdlib/stats/base/dists/halfnormal/entropy - Differential entropy
• @stdlib/stats/base/dists/halfnormal/skewness - Skewness
• @stdlib/stats/base/dists/halfnormal/kurtosis - Excess kurtosis

Generating Functions

• @stdlib/stats/base/dists/halfnormal/mgf - Moment-generating function (MGF)

Constructor and Utilities

• @stdlib/stats/base/dists/halfnormal/ctor - Distribution constructor

Main Package

• @stdlib/stats/base/dists/halfnormal - Main package with exports and documentation

Related Issues

• [RFC]: Add support for half-normal distribution @stdlib/stats/base/dists/halfnormal #8205 - Original RFC for half-normal distribution support
• [RFC]: adding new statistical distributions ( tracking issue ) #6951 - Related issue mentioned in [RFC]: Add support for half-normal distribution @stdlib/stats/base/dists/halfnormal #8205

Questions

• Are there any additional distribution-specific functions that should be included beyond the standard set?
• Should we implement any specialized constants related to the half-normal distribution?

Other

No.

Checklist

• I have read and understood the Code of Conduct.
• Searched for existing issues and pull requests.
• The issue name begins with RFC:.