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) 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) . 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.

autorelevate

autorelevate package implements the autorelevated family of probability distributions. The autorelevated family is obtained by applying the autorelevation transformation of Krakowski (1973) and Dileepkumar and Sankaran (2022) to a baseline lifetime distribution. Ten baseline distributions, namely Weibull, Lomax, Burr XII, Gompertz, Log-Logistic, Chen, Exponentiated Exponential, Power Lindley, Log-normal, and Gamma constitute the members of the family. The Weibull member ("Autorelevated Weibull") is studied in detail by Dileep Kumar, Shabeer, and Sankaran (2025), whose results this package implements and generalizes.

Installation

# install.packages("devtools")
devtools::install_github("vksharma-bhu/autorelevate")

Example

library(autorelevate)

# Simulate from an Autorelevated Weibull distribution
set.seed(1)
x <- rautorelevate(200, dist = "weibull", p1 = 0.5, p2 = 1.5)

# Fit by maximum likelihood
fit <- fit_autorelevate(x, dist = "weibull", method = "mle")
summary(fit)
plot(fit)

# Compare all ten baseline distributions by information criteria
compare_families(x)

# A real dataset is bundled with the package
data(bladder_cancer)
ttt_plot(bladder_cancer)
compare_families(bladder_cancer)

Citation

See citation("autorelevate") to cite the package itself. The underlying methodological references (Krakowski, 1973; Dileepkumar & Sankaran, 2022; Dileep Kumar, Shabeer, & Sankaran, 2025; Sharma, Pal, Bhardwaj, & Tyagi, 2026, submitted) are listed in ?autorelevate-package and throughout the function documentation.