BetaDanish - The Beta-Danish Distribution for Lifetime Data Analysis

Implements the four-parameter Beta-Danish distribution and its three-parameter submodel for survival and reliability analysis, based on Ahmad and Danish (2025) <doi:10.2478/jamsi-2025-0010>. Provides functions for density, distribution, quantile, hazard, and random generation. Includes maximum likelihood estimation for complete and right-censored data, goodness-of-fit assessment, comparison with standard lifetime distributions, and publication-quality visualizations. Advanced modules support Accelerated Failure Time (AFT) regression, mixture and promotion-time cure models, and competing risks analysis.