Bayesian Point Estimation Using Lindley's Approximation Under Censoring Schemes
Overview
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.
Initial Release
- Implemented core Lindley approximation engine for Bayesian point estimation
- Added support for 23 censoring and truncation schemes
- Implemented 8 loss functions for Bayes estimation
- Added automatic numerical derivative computation (first, second, third-order)
- Implemented comprehensive S3 methods for lindleyfit objects
- Added goodness-of-fit statistics (KS, AD, CvM, Watson, Chi-square)
- Implemented residual analysis (Cox-Snell, Martingale, Deviance, Pearson, Generalized, Randomized quantile)
- Added visualization functions (posterior surfaces, likelihood profiles, QQ/PP plots, residual plots)
- Implemented prediction utilities (quantiles, survival, hazard, cumulative hazard)
- Added simulation utilities for all censoring schemes
- Implemented model selection criteria (AIC, AICc, BIC, HQIC, CAIC, KIC)
Show all changes in 0.1.0Hide the rest of the changes in 0.1.0
- Added support for multiple prior distributions (Gamma, Beta, Normal, Uniform, Lognormal, Inverse Gamma, Weibull, Exponential, Jeffreys)
- Implemented modular, extensible architecture for adding new censoring schemes
- Added comprehensive error handling and validation
- Created roxygen2 documentation for all functions
From NEWS.md in the release
Install
Health
- OK13 OK2026-09-08
- ERROR12 OK, 1 ERROR2026-09-07
- OK7 OK2026-08-07
Documentation
- Help pages
- 152 (75 internal)includes a package overview page
- Examples that run
- 100%2 run in a plain check
- Exported functions with examples
- 5%
- Documented parameters
- 100%
- Return-value docs
- 100%
- Help pages citing references
- 1%
Downloads
Dependencies
Installing UniLindleyApprox adds 1 package (0 with compiled code, 74 KB of source tarballs). Heaviest: numDeriv 74 KB.
Code & Tests
People & History
- 0.1.0Latest2026-08-06 · current release
- RR 4.6.0 released · 2026-04-24
Package metadata
- First published
- 2026-08-06
- Total releases
- 1 / 1 yrs
- License
- GPL-3 OSI
- Minimum R
- ≥ 4.0.0
- Download size
- 69 KB
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