Shared Frailty Regression Models with Inverse Gaussian, Generalized Lindley, and Gamma Frailty Distributions // Implements shared frailty regression models for survival data under eight censoring mechanisms: exact, right censoring (Kalbfleisch and Prentice, 2002), left censoring, interval censoring (Sun, 2006), progressive Type I censoring, and progressive Type II censoring (Balakrishnan and Aggarwala, 2000 doi:10.1007/978-1-4612-1334-5). Combines four frailty distributions -- Gamma (Clayton, 1978), Inverse Gaussian (Hougaard, 1984), and two variants of the Generalized Lindley (GL) distribution: GL Type 1, a two-component gamma mixture with distribution-specific scale/shape linkage (Pandey, Hanagal, and Tyagi, 2022), and GL Type 2, a two-component gamma mixture with a common rate parameter (Pandey and Tyagi, 2021 doi:10.1134/S1995080222010140) -- with two baseline hazard distributions: the two-parameter Weibull distribution (Weibull, 1951) and the three-parameter Generalized (Exponentiated) Weibull distribution (Mudholkar and Srivastava, 1993 doi:10.1109/24.229504). A no-frailty baseline-only model is also supported for nested model comparison. Maximum likelihood estimation is conducted using Newton-Raphson and Broyden- Fletcher-Goldfarb-Shanno (BFGS) algorithms via the 'maxLik' package (Henningsen and Toomet, 2011 doi:10.1007/s00180-010-0217-1). Provides standard errors, confidence intervals, hypothesis tests, Akaike Information Criterion (AIC, Akaike, 1974 doi:10.1109/TAC.1974.1100705), Bayesian Information Criterion (BIC, Schwarz, 1978 doi:10.1214/aos/1176344136), corrected Akaike Information Criterion (AICc, Hurvich and Tsai, 1989), Hannan-Quinn Information Criterion (HQIC, Hannan and Quinn, 1979), a bootstrap approximation of the Widely Applicable Information Criterion (WAIC, Watanabe, 2010), k-fold cross-validation, frailty variance estimation, survival, hazard, median, risk, and marginal predictions, Cox-Snell (Cox and Snell, 1968), martingale (Barlow and Prentice, 1988), and deviance residuals with a Kolmogorov-Smirnov goodness-of-fit test, influence diagnostics (leverage, Cook's distance, difference in fits (DFFITS), difference in betas (DFBETAS); Belsley, Kuh, and Welsch, 1980), random data generation under all eight censoring mechanisms, a Monte Carlo simulation-study function, and a diagnostic and survival plotting suite.