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.
Documentation:
Downloads:
Linking:
Please use the canonical form
https://CRAN.R-project.org/package=autorelevate
to link to this page.