Package: UniLindleyApprox 0.1.0

UniLindleyApprox: Bayesian Point Estimation Using Lindley's Approximation Under Censoring Schemes

Performs Bayesian point estimation using Lindley's Approximation (1980) <doi:10.1111/j.2517-6161.1980.tb01102.x> for arbitrary univariate probability distributions under numerous censoring and truncation schemes. Users supply the probability density function (PDF), cumulative distribution function (CDF), survival function, log-prior density, initial parameter vector, support bounds, and observed data; the package automatically computes Bayesian point estimates under various loss functions using Lindley's approximation. Supported schemes include complete data, right censoring, left censoring, interval censoring, random censoring, block random censoring, Type-I censoring, Type-II censoring, progressive Type-II censoring, progressive first failure censoring, joint Type-I censoring, joint Type-II censoring, balanced joint progressive Type-II censoring, hybrid censoring, hybrid Type-I censoring, hybrid Type-II censoring, Type-I hybrid censoring, Type-II progressively hybrid censoring, doubly Type-II censoring, middle censoring, right truncation, and left truncation. The package computes posterior expectations of arbitrary smooth functions, supports multiple loss functions (squared error loss function (SELF), weighted squared error loss function (WSELF), modified quadratic squared error loss function (MQSELF), precautionary loss function (PLF), entropy loss function (ELF), linear-exponential (LINEX), generalized entropy loss function (GELF), Kullback-Leibler loss function (K-Loss), and user-defined), provides model selection criteria (Akaike information criterion (AIC), Bayesian information criterion (BIC), corrected Akaike information criterion (AICc), Hannan-Quinn information criterion (HQIC), consistent Akaike information criterion (CAIC), Kullback information criterion (KIC)), goodness-of-fit statistics (Kolmogorov-Smirnov, Anderson-Darling, Cramer-von Mises, Watson, Chi-square), residual analysis (Cox-Snell, Martingale, Deviance, Pearson, Generalized, Randomized quantile), comprehensive visualization tools, prediction utilities, and simulation functions for benchmarking estimators. Methods are described in Lindley (1980) <doi:10.1111/j.2517-6161.1980.tb01102.x>, Tierney and Kadane (1986) <doi:10.2307/2234555>, Tierney, Kass, and Kadane (1989) <doi:10.2307/2335663>, Nagar, Kumar, and Krishna (2026) <doi:10.59467/IJASS.2026.22.1>, Goel, Kumar, and Krishna (2026, "Estimation in power Lindley distributions using balanced joint progressively Type-II censored data"), Wu and Kus (2009) <doi:10.1016/j.csda.2009.03.010>, Goel and Krishna (2026) <doi:10.1007/s13198-026-03208-w>, Balakrishnan and Aggarwala (2000, ISBN:978-1-4612-1334-5), Mondal and Kundu (2020) <doi:10.1080/03610926.2018.1554128>, Ding and Gui (2023) <doi:10.3390/math11092003>, Prajapati, Mitra, and Kundu (2019) <doi:10.1007/s13571-018-0167-0>, Yadav, Jaiswal, and Yadav (2026) <doi:10.1007/s11135-026-02647-8>, Iyer, Jammalamadaka, and Kundu (2008) <doi:10.1016/j.jspi.2007.03.062>, Banerjee and Kundu (2008) <doi:10.1109/TR.2008.916890>, and Kundu and Joarder (2006) <doi:10.1016/j.csda.2005.05.002>.

Authors:Shikhar Tyagi [aut, cre], Arvind Pandey [aut], Bhupendra Singh [aut], Vrijesh Tripathi [aut]