autorelevate - The Autorelevated Family of Probability Distributions and Estimation Methods

Implements the autorelevated family of probability distributions, obtained by applying the autorelevation transformation of Krakowski (1973) <doi:10.1051/ro/197307V201071> and Dileepkumar and Sankaran (2022) to ten baseline probability distributions: Weibull, Lomax, Burr XII, Gompertz, Log-Logistic, Chen, Exponentiated Exponential, Power Lindley, Log-normal, and Gamma. The Weibull member of the family is studied in detail by Dileep Kumar, Shabeer, and Sankaran (2025) <doi:10.1080/01966324.2026.2665479>. The Lomax member is studied by Sharma, Pal, Bhardwaj, and Tyagi (2026, submitted), who establish its upside-down bathtub hazard shape. Supplies vectorized density, distribution, survival, hazard, quantile (via the negative branch of the Lambert W function), and random-generation functions for all ten members of the family. It also implements Maximum Likelihood, Maximum Product of Spacings, Least Squares, Weighted Least Squares, and Cramer-von Mises estimation methods along with a Kolmogorov-Smirnov goodness-of-fit test, a Total Time on Test plot, and model selection by AIC, BIC, CAIC, and HQIC. It also includes a bundled bladder cancer remission dataset (Lee and Wang, 2003) for illustration.