Alpha-Power Hazard Regression Models for Survival Data

Implements the alpha-power hazard model and regression frameworks for survival data based on the flexible hazard rate function h(x; alpha, beta) = alpha^x + x^(beta-1) (Pal et al., 2026 ). Provides standard distribution functions (d, p, q, r, h, H, s) and distributional properties including raw/central moments, variance, skewness, kurtosis, quantile statistics (Bowley's skewness, Moors's kurtosis), Lambert W hazard rate function minimum (Corless et al., 1996), order statistics, and stochastic ordering (Shaked & Shanthikumar, 1994). Computes five classical estimation methods for baseline parameters: Maximum Likelihood Estimation (Casella & Berger, 2002), Least Squares Estimation (Swain et al., 1988), Weighted Least Squares Estimation (Styan, 1973), Maximum Product of Spacings Estimation (Cheng & Amin, 1983 ), and Cramer-von Mises Estimation (Macdonald, 1971). Supports four hazard regression models (M1-M4) within proportional hazards and parametric frameworks across uncensored data, right censoring, left censoring, interval censoring, and progressive Type-I and Type-II censoring schemes (Lee & Wang, 2003; Lawless, 2011; Balakrishnan & Aggarwala, 2000). Includes comprehensive model diagnostics, Cox-Snell, martingale, deviance, standardized, and studentized residuals, leverage, Cook's distance, DFFITS, DFBETAS, model comparisons (AIC, BIC, WAIC), k-fold cross-validation, prediction suites, random data generators, and an eight-panel diagnostic visualization suite.