UniLindleyApprox

Bayesian Point Estimation Using Lindley's Approximation Under Censoring Schemes

UniLindleyApprox is a CRAN-quality R package for performing Bayesian parameter estimation using Lindley's Approximation (1980) for arbitrary univariate probability distributions under complete, censored, and truncated data.

Features

• Generalized Framework: Works with any user-defined univariate probability distribution
• Multiple Censoring Schemes: Supports 23 different censoring and truncation schemes
• Loss Functions: Computes Bayes estimates under 8 different loss functions
• Automatic Derivatives: Numerical computation of first, second, and third-order derivatives
• Comprehensive Diagnostics: Goodness-of-fit statistics, residual analysis, model selection criteria
• Visualization: Diagnostic plots including posterior surfaces, likelihood profiles, QQ plots
• Simulation Utilities: Functions for benchmarking estimators under various censoring schemes

Installation

# Install from CRAN (when available)
install.packages("UniLindleyApprox")

# Install development version
devtools::install_github("username/UniLindleyApprox")

Quick Start

library(UniLindleyApprox)

# Define probability functions for exponential distribution
dexp_custom <- function(x, theta) dexp(x, rate = theta[1])
pexp_custom <- function(x, theta) pexp(x, rate = theta[1])
sexp_custom <- function(x, theta) 1 - pexp(x, rate = theta[1])

# Define log-prior (Gamma prior for rate)
logprior <- function(theta) {
  dgamma(theta[1], shape = 2, rate = 1, log = TRUE)
}

# Generate data
set.seed(123)
x <- rexp(50, rate = 2)

# Fit model using Lindley's approximation
fit <- lindley_fit(
  data = x,
  pdf = dexp_custom,
  cdf = pexp_custom,
  survival = sexp_custom,
  log_prior = logprior,
  theta0 = c(1),
  scheme = "complete",
  loss = "SELF"
)

# View results
print(fit)
summary(fit)

# Diagnostic plots
plot(fit)

# Goodness-of-fit statistics
gof_stats(fit)

Supported Censoring Schemes

1. Complete data
2. Right censoring
3. Left censoring
4. Interval censoring
5. Random censoring
6. Block random censoring
7. Type-I censoring
8. Type-II censoring
9. Progressive Type-II censoring
10. Progressive first failure censoring
11. Joint Type-I censoring
12. Joint Type-II censoring
13. Balanced joint progressive Type-II censoring
14. Hybrid censoring
15. Hybrid Type-I censoring
16. Hybrid Type-II censoring
17. Type-I hybrid censoring
18. Type-II progressively hybrid censoring
19. Doubly Type-II censoring
20. Middle censoring
21. Right truncation
22. Left truncation

Supported Loss Functions

• SELF: Squared Error Loss Function
• WSELF: Weighted Squared Error Loss Function
• MQSELF: Modified Quadratic Squared Error Loss Function
• PLF: Precautionary Loss Function
• ELF: Entropy Loss Function
• LINEX: Linear Exponential Loss Function
• GELF: General Entropy Loss Function
• K-Loss: K-Loss Function

Model Selection Criteria

• AIC (Akaike Information Criterion)
• AICc (Corrected AIC)
• BIC (Bayesian Information Criterion)
• HQIC (Hannan-Quinn Information Criterion)
• CAIC (Consistent AIC)
• KIC (Kullback Information Criterion)

Goodness-of-Fit Statistics

• Kolmogorov-Smirnov statistic
• Anderson-Darling statistic
• Cramér-von Mises statistic
• Watson statistic
• Chi-square statistic
• Mean Squared Error
• Mean Absolute Error
• Root Mean Squared Error

Residual Types

• Cox-Snell residuals
• Martingale residuals
• Deviance residuals
• Pearson residuals
• Generalized residuals
• Randomized quantile residuals

Citation

If you use UniLindleyApprox in your research, please cite:

Tyagi, S., Pandey, A., Singh, B., & Tripathi, V. (2024). UniLindleyApprox: 
Bayesian Point Estimation Using Lindley's Approximation Under Censoring Schemes. 
R package version 0.1.0.

References

• Lindley, D. V. (1980). Approximate Bayesian methods. Trabajos de Estadistica y de Investigacion Operativa, 31(1), 223-245.
• Tierney, L., & Kadane, J. B. (1986). Accurate approximations for posterior moments and marginal densities. Journal of the American Statistical Association, 81(393), 82-86.
• Tierney, L., Kass, R. E., & Kadane, J. B. (1989). Fully exponential Laplace approximations to expectations and variances of nonpositive functions. Journal of the American Statistical Association, 84(407), 710-716.

License

GPL-3

Authors

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

Related Packages

• UniCensor: Generalized generation of censored and truncated random samples
• UniCensorEM: Generalized maximum likelihood estimation using the EM algorithm
• UniIS: Generalized Bayesian and likelihood inference using importance sampling

These packages complement each other while sharing a consistent interface and design philosophy.