Package {UniLindleyApprox}

Type:	Package
Title:	Bayesian Point Estimation Using Lindley's Approximation Under Censoring Schemes
Version:	0.1.0
Description:	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>.
License:	GPL-3
Depends:	R (≥ 4.0.0)
Imports:	stats, graphics, grDevices, utils, methods, numDeriv, MASS
Suggests:	testthat (≥ 3.0.0), ggplot2, future, parallel, knitr, rmarkdown
Config/testthat/edition:	3
Encoding:	UTF-8
Language:	en-US
RoxygenNote:	7.3.3
VignetteBuilder:	knitr
NeedsCompilation:	no
Packaged:	2026-07-29 00:54:59 UTC; shikhar tyagi
Author:	Shikhar Tyagi [aut, cre], Arvind Pandey [aut], Bhupendra Singh [aut], Vrijesh Tripathi [aut]
Maintainer:	Shikhar Tyagi <shikhar1093tyagi@gmail.com>
Repository:	CRAN
Date/Publication:	2026-08-06 13:50:13 UTC

UniLindleyApprox: Bayesian Point Estimation Using Lindley's Approximation

Description

The UniLindleyApprox package provides a generalized framework for Bayesian parameter estimation using Lindley's Approximation (1980) for arbitrary univariate probability distributions under complete, censored, and truncated data.

Main Function

The main function is lindley_fit which performs Bayesian estimation using Lindley's approximation.

Censoring Schemes

The package supports 23 censoring and truncation schemes including:

complete

Complete (uncensored) data

right

Right censoring

left

Left censoring

interval

Interval censoring

random

Random censoring

type1

Type-I censoring

type2

Type-II censoring

progressive_type2

Progressive Type-II censoring

progressive_first_failure

Progressive first failure censoring

joint_type1

Joint Type-I censoring

joint_type2

Joint Type-II censoring

bjpt2

Balanced joint progressive Type-II censoring

hybrid

Hybrid censoring

hybrid_type1

Hybrid Type-I censoring

hybrid_type2

Hybrid Type-II censoring

type1_hybrid

Type-I hybrid censoring

type2_progressively_hybrid

Type-II progressively hybrid censoring

doubly_type2

Doubly Type-II censoring

middle

Middle censoring

right_truncation

Right truncation

left_truncation

Left truncation

Loss Functions

The package computes Bayes estimates under various 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

Prior Distributions

Supported prior distributions include:

Gamma

log_prior_gamma

Beta

log_prior_beta

Normal

log_prior_normal

Uniform

log_prior_uniform

Lognormal

log_prior_lognormal

Inverse Gamma

log_prior_invgamma

Weibull

log_prior_weibull

Exponential

log_prior_exponential

Jeffreys

log_prior_jeffreys

Model Selection

Model selection criteria include AIC, AICc, BIC, HQIC, CAIC, and KIC.

Goodness-of-Fit

Goodness-of-fit statistics include KS, AD, CvM, Watson, and Chi-square tests.

Residuals

Residual types include Cox-Snell, Martingale, Deviance, Pearson, Generalized, and Randomized quantile residuals.

Visualization

Visualization functions include posterior surface plots, likelihood profiles, QQ plots, PP plots, and residual plots.

Simulation

Simulation utilities are available for all censoring schemes for benchmarking.

Author(s)

Maintainer: Shikhar Tyagi shikhar1093tyagi@gmail.com (ORCID)

Authors:

• Arvind Pandey arvindmzu@gmail.com

• Bhupendra Singh bhupendra.rana@gmail.com

• Vrijesh Tripathi vrijesh.tripathi@uwi.edu

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.

AIC Method for lindleyfit Objects

Description

AIC Method for lindleyfit Objects

Usage

## S3 method for class 'lindleyfit'
AIC(object, ...)

Arguments

Value

AIC value.

AIC Method for lindleyfit Objects Corrected Akaike Information Criterion (AICc)

Description

Computes the corrected AIC for fitted models.

Usage

AICc(object, ...)

Arguments

Value

AICc value.

AICc Method for lindleyfit Objects

Description

AICc Method for lindleyfit Objects

Usage

## S3 method for class 'lindleyfit'
AICc(object, ...)

Arguments

Value

AICc value.

BIC Method for lindleyfit Objects

Description

BIC Method for lindleyfit Objects

Usage

## S3 method for class 'lindleyfit'
BIC(object, ...)

Arguments

Value

BIC value.

Consistent Akaike Information Criterion (CAIC)

Description

Computes the CAIC for fitted models.

Usage

CAIC(object, ...)

Arguments

Value

CAIC value.

CAIC Method for lindleyfit Objects

Description

Consistent AIC.

Usage

## S3 method for class 'lindleyfit'
CAIC(object, ...)

Arguments

Value

CAIC value.

Hannan-Quinn Information Criterion (HQIC)

Description

Computes the HQIC for fitted models.

Usage

HQIC(object, ...)

Arguments

Value

HQIC value.

HQIC Method for lindleyfit Objects

Description

Hannan-Quinn Information Criterion.

Usage

## S3 method for class 'lindleyfit'
HQIC(object, ...)

Arguments

Value

HQIC value.

Kullback Information Criterion (KIC)

Description

Computes the KIC for fitted models.

Usage

KIC(object, ...)

Arguments

Value

KIC value.

KIC Method for lindleyfit Objects

Description

Kullback Information Criterion.

Usage

## S3 method for class 'lindleyfit'
KIC(object, ...)

Arguments

Value

KIC value.

Autoplot Method for lindleyfit Objects

Description

Creates a comprehensive set of diagnostic plots using ggplot2 if available.

Usage

autoplot.lindleyfit(object, which = 1:4, ...)

Arguments

Value

A ggplot object or list of ggplot objects.

Bayes Estimate Under Custom Loss Function

Description

Bayes Estimate Under Custom Loss Function

Usage

bayes_custom(fit, loss_fun, ...)

Bayes Estimate Under ELF

Description

Bayes Estimate Under ELF

Usage

bayes_elf(fit)

Compute Bayes Estimate Under Specified Loss Function

Description

Computes the Bayes estimate that minimizes the expected loss.

Usage

bayes_estimate(fit, loss = "SELF", ...)

Arguments

Value

Bayes estimate under specified loss function.

Bayes Estimate Under GELF

Description

Bayes Estimate Under GELF

Usage

bayes_gelf(fit, q = 2)

Bayes Estimate Under K-Loss

Description

Bayes Estimate Under K-Loss

Usage

bayes_kloss(fit)

Bayes Estimate Under LINEX

Description

Bayes Estimate Under LINEX

Usage

bayes_linex(fit, a = 1)

Bayes Estimate Under MQSELF

Description

Bayes Estimate Under MQSELF

Usage

bayes_mqself(fit, k = 1)

Bayes Estimate Under PLF

Description

Bayes Estimate Under PLF

Usage

bayes_plf(fit, a = 1)

Bayes Estimate Under SELF

Description

Bayes Estimate Under SELF

Usage

bayes_self(fit)

Bayes Estimate Under WSELF

Description

Bayes Estimate Under WSELF

Usage

bayes_wself(fit, w = 1)

Check Convergence

Description

Checks if optimization converged successfully.

Usage

check_convergence(convergence, method)

Arguments

Value

Logical indicating convergence.

Check Parameter Support

Description

Checks if parameters are within valid support.

Usage

check_support(theta, support)

Arguments

Value

Logical indicating validity.

Coefficient Method for lindleyfit Objects

Description

Extracts the Bayes estimate.

Usage

## S3 method for class 'lindleyfit'
coef(object, ...)

Arguments

Value

Parameter estimates.

Compare Predictions

Description

Compares predictions from multiple fitted models.

Usage

compare_predictions(..., newdata, type = "density")

Arguments

Value

Data frame with predictions from each model.

Numerical Derivatives for Lindley Approximation

Description

Computes first, second, and third-order derivatives of log-likelihood and log-posterior functions using numerical differentiation.

Usage

compute_derivatives(fun, theta, control = lindley.control(), ...)

Arguments

Value

A list containing gradient, Hessian, and third-order derivatives.

Compute Information Matrix

Description

Computes the observed information matrix from the Hessian.

Usage

compute_info_matrix(hessian)

Arguments

Value

Information matrix.

Compute Lindley Correction Terms

Description

Computes the correction terms for Lindley's approximation.

Usage

compute_lindley_correction(
  theta_map,
  info_inv,
  third_deriv,
  logpost_fun,
  g_fun,
  theta_dim,
  control = lindley.control()
)

Arguments

Value

Lindley approximation result.

Posterior Computation for Lindley Approximation

Description

Constructs the log-posterior function and computes posterior mode.

Usage

compute_posterior(loglik_fun, log_prior, theta0, control = lindley.control())

Arguments

Value

A list containing log-posterior function and posterior mode.

Compute Sample Size

Description

Computes effective sample size based on censoring scheme.

Usage

compute_sample_size(data, scheme)

Arguments

Value

Sample size.

Compute Third-Order Derivatives

Description

Computes third-order partial derivatives for Lindley approximation.

Usage

compute_third_derivatives(
  fun,
  theta,
  eps = 1e-05,
  deriv_method = "numDeriv",
  ...
)

Arguments

Value

Third-order derivative tensor (array).

Condition Number of a Matrix

Description

Computes the condition number of a matrix.

Usage

cond(x, ...)

Arguments

Value

Condition number.

Likelihood Construction for Censoring Schemes

Description

Constructs the log-likelihood function for various censoring schemes.

Usage

construct_loglikelihood(data, pdf, cdf, survival, scheme, scheme_params = NULL)

Arguments

Value

Log-likelihood function.

Create Parameter Grid

Description

Creates a grid of parameter values for surface plots.

Usage

create_param_grid(theta1_range, theta2_range, n = 50)

Arguments

Value

List with x, y, and grid values.

Extract Diagnostic Information

Description

Extracts computational and convergence diagnostics from a fitted model.

Usage

diagnostics(object, ...)

Arguments

Value

Diagnostic list.

Diagnostics Method for lindleyfit Objects

Description

Computes diagnostic information for the fitted model.

Usage

## S3 method for class 'lindleyfit'
diagnostics(object, ...)

Arguments

Value

A list of diagnostic information.

Extract Observed Data

Description

Extracts observed data points based on censoring scheme.

Usage

extract_observed(data, scheme)

Arguments

Value

Observed data vector.

Find Posterior Mode

Description

Optimizes the log-posterior to find the MAP estimate.

Usage

find_posterior_mode(logpost_fun, theta0, control = lindley.control())

Arguments

Value

Optimization result.

Find Root

Description

Finds root of a function using numerical methods.

Usage

find_root(fun, interval, ...)

Arguments

Value

Root value.

Finite Difference Gradient

Description

Computes gradient using central finite differences.

Usage

finite_diff_grad(fun, theta, eps = 1e-06, ...)

Arguments

Value

Gradient vector.

Finite Difference Hessian

Description

Computes Hessian matrix using central finite differences.

Usage

finite_diff_hessian(fun, theta, eps = 1e-06, ...)

Arguments

Value

Hessian matrix.

Finite Difference Third-Order Derivative

Description

Computes a single third-order partial derivative using finite differences.

Usage

finite_diff_third(fun, theta, i, j, k, eps = 1e-06, ...)

Arguments

Value

Third-order partial derivative value.

Fitted Method for lindleyfit Objects

Description

Computes fitted values (density, CDF, survival) at data points.

Usage

## S3 method for class 'lindleyfit'
fitted(object, type = "density", ...)

Arguments

Value

Fitted values.

Format Parameter Names

Description

Formats parameter names for display.

Usage

format_param_names(theta, prefix = "theta")

Arguments

Value

Character vector of parameter names.

Anderson-Darling Statistic

Description

Computes the Anderson-Darling goodness-of-fit statistic.

Usage

gof_ad(fit, ...)

Arguments

Value

AD statistic value.

Chi-Square Goodness-of-Fit Statistic

Description

Computes the chi-square goodness-of-fit statistic for binned data.

Usage

gof_chisq(fit, bins = NULL, ...)

Arguments

Value

Chi-square statistic and p-value.

Cramér-von Mises Statistic

Description

Computes the Cramér-von Mises goodness-of-fit statistic.

Usage

gof_cvm(fit, ...)

Arguments

Value

CvM statistic value.

Kolmogorov-Smirnov Statistic

Description

Computes the Kolmogorov-Smirnov goodness-of-fit statistic.

Usage

gof_ks(fit, ...)

Arguments

Value

KS statistic value.

Goodness-of-Fit Statistics

Description

Computes various goodness-of-fit statistics for the fitted model.

Usage

gof_stats(fit, ...)

Arguments

Value

A list of goodness-of-fit statistics.

Watson Statistic

Description

Computes the Watson goodness-of-fit statistic (a variant of Cramér-von Mises).

Usage

gof_watson(fit, ...)

Arguments

Value

Watson statistic value.

Create Independent Product Prior

Description

Creates a log-prior for independent priors on each parameter.

Usage

independent_prior(prior_list, ...)

Arguments

Value

Combined log-prior function.

Validate Hessian Positive Definiteness

Description

Checks if a Hessian matrix is positive definite.

Usage

is_positive_definite(hessian, tol = 1e-10)

Arguments

Value

Logical indicating positive definiteness.

Control Parameters for Lindley Approximation

Description

Creates a list of control parameters for the Lindley approximation algorithm.

Usage

lindley.control(
  method = "BFGS",
  maxit = 1000,
  reltol = 1e-08,
  abstol = 1e-10,
  hessian = TRUE,
  third_deriv = TRUE,
  deriv_method = "numDeriv",
  eps = 1e-06,
  parallel = FALSE,
  ncores = 2,
  verbose = TRUE,
  trace = 0,
  check_prior = TRUE,
  check_support = TRUE,
  check_hessian = TRUE,
  cache_derivatives = TRUE,
  use_analytical = TRUE
)

Arguments

Value

A list of control parameters for use in lindley_fit.

Examples

ctrl <- lindley.control(method = "BFGS", maxit = 500, verbose = FALSE)

Core Lindley Approximation Engine

Description

Implements Lindley's approximation for computing posterior expectations of arbitrary smooth functions of parameters.

Usage

lindley_approximation(
  logpost_fun,
  theta_map,
  hessian,
  third_deriv,
  g_fun = NULL,
  theta_dim,
  control = lindley.control()
)

Arguments

Value

Posterior expectation approximation.

Bayesian Estimation Using Lindley's Approximation

Description

Main function for performing Bayesian parameter estimation using Lindley's approximation for arbitrary univariate distributions under various censoring schemes.

Usage

lindley_fit(
  data,
  pdf,
  cdf,
  survival,
  log_prior,
  theta0,
  scheme = "complete",
  loss = "SELF",
  control = lindley.control(),
  scheme_params = NULL,
  ...
)

Arguments

Value

An object of class lindleyfit containing:

map_estimate

Posterior mode (MAP estimate)

bayes_estimate

Bayes estimate under specified loss function

posterior_mean

Posterior mean approximation

hessian

Hessian matrix at posterior mode

gradient

Gradient vector at posterior mode

third_deriv

Third-order derivative tensor

log_likelihood

Log-likelihood at MAP

log_posterior

Log-posterior at MAP

convergence

Optimization convergence status

iterations

Number of optimization iterations

data

Input data

scheme

Censoring scheme used

loss

Loss function used

control

Control parameters

elapsed_time

Computation time

Supported Censoring Schemes

complete

Complete (uncensored) data

right

Right censoring

left

Left censoring

interval

Interval censoring

random

Random censoring

type1

Type-I censoring

type2

Type-II censoring

progressive_type2

Progressive Type-II censoring

progressive_first_failure

Progressive first failure censoring

joint_type1

Joint Type-I censoring

joint_type2

Joint Type-II censoring

bjpt2

Balanced joint progressive Type-II censoring

hybrid

Hybrid censoring

hybrid_type1

Hybrid Type-I censoring

hybrid_type2

Hybrid Type-II censoring

type1_hybrid

Type-I hybrid censoring

type2_progressively_hybrid

Type-II progressively hybrid censoring

doubly_type2

Doubly Type-II censoring

middle

Middle censoring

right_truncation

Right truncation

left_truncation

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

Examples

# Exponential distribution with complete data
set.seed(123)
x <- rexp(50, rate = 2)

# Define probability functions
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)
}

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

# Print results
print(fit)

Log-Likelihood Method for lindleyfit Objects

Description

Log-Likelihood Method for lindleyfit Objects

Usage

## S3 method for class 'lindleyfit'
logLik(object, ...)

Arguments

Value

Log-likelihood value.

Create Multivariate Normal Prior

Description

Create Multivariate Normal Prior

Usage

log_prior_mvn(theta, mean, sigma, ...)

Arguments

Value

Log-prior density.

Prior Distributions for Bayesian Estimation

Description

Provides log-prior density functions for common prior distributions.

Jeffreys prior is proportional to sqrt(det(I(theta))), where I(theta) is the Fisher information matrix. For common distributions, this simplifies to known forms.

Usage

log_prior_gamma(theta, shape = 1, rate = 1, ...)

log_prior_beta(theta, shape1 = 1, shape2 = 1, ...)

log_prior_normal(theta, mean = 0, sd = 1, ...)

log_prior_uniform(theta, min = 0, max = 1, ...)

log_prior_lognormal(theta, meanlog = 0, sdlog = 1, ...)

log_prior_invgamma(theta, shape = 1, scale = 1, ...)

log_prior_weibull(theta, shape = 1, scale = 1, ...)

log_prior_exponential(theta, rate = 1, ...)

log_prior_jeffreys(theta, distribution = "exponential", ...)

Arguments

Value

Log-prior density value.

Log-prior density.

Log-prior density.

Log-prior density.

Log-prior density.

Log-prior density.

Log-prior density.

Log-prior density.

Log-prior density.

Log-prior density.

Compute Log-Sum-Exp

Description

Computes log(sum(exp(x))) in a numerically stable way.

Usage

log_sum_exp(x)

Arguments

Value

Log-sum-exp value.

Log-Likelihood for Balanced Joint Progressive Type-II Censoring

Description

Log-Likelihood for Balanced Joint Progressive Type-II Censoring

Usage

loglik_bjpt2(theta, data, pdf, cdf, survival, scheme_params = NULL)

Arguments

Value

Log-likelihood value.

Log-Likelihood for Complete Data

Description

Log-Likelihood for Complete Data

Usage

loglik_complete(theta, data, pdf, cdf, survival, scheme_params = NULL)

Arguments

Value

Log-likelihood value.

Log-Likelihood for Doubly Type-II Censoring

Description

Log-Likelihood for Doubly Type-II Censoring

Usage

loglik_doubly_type2(theta, data, pdf, cdf, survival, scheme_params = NULL)

Arguments

Value

Log-likelihood value.

Log-Likelihood for Hybrid Censoring

Description

Log-Likelihood for Hybrid Censoring

Usage

loglik_hybrid(theta, data, pdf, cdf, survival, scheme_params = NULL)

Arguments

Value

Log-likelihood value.

Log-Likelihood for Hybrid Type-I Censoring

Description

Log-Likelihood for Hybrid Type-I Censoring

Usage

loglik_hybrid_type1(theta, data, pdf, cdf, survival, scheme_params = NULL)

Arguments

Value

Log-likelihood value.

Log-Likelihood for Hybrid Type-II Censoring

Description

Log-Likelihood for Hybrid Type-II Censoring

Usage

loglik_hybrid_type2(theta, data, pdf, cdf, survival, scheme_params = NULL)

Arguments

Value

Log-likelihood value.

Log-Likelihood for Interval Censoring

Description

Log-Likelihood for Interval Censoring

Usage

loglik_interval(theta, data, pdf, cdf, survival, scheme_params = NULL)

Arguments

Value

Log-likelihood value.

Log-Likelihood for Joint Type-I Censoring

Description

Log-Likelihood for Joint Type-I Censoring

Usage

loglik_joint_type1(theta, data, pdf, cdf, survival, scheme_params = NULL)

Arguments

Value

Log-likelihood value.

Log-Likelihood for Joint Type-II Censoring

Description

Log-Likelihood for Joint Type-II Censoring

Usage

loglik_joint_type2(theta, data, pdf, cdf, survival, scheme_params = NULL)

Arguments

Value

Log-likelihood value.

Log-Likelihood for Left Censoring

Description

Log-Likelihood for Left Censoring

Usage

loglik_left(theta, data, pdf, cdf, survival, scheme_params = NULL)

Arguments

Value

Log-likelihood value.

Log-Likelihood for Left Truncation

Description

Log-Likelihood for Left Truncation

Usage

loglik_left_truncation(theta, data, pdf, cdf, survival, scheme_params = NULL)

Arguments

Value

Log-likelihood value.

Log-Likelihood for Middle Censoring

Description

Log-Likelihood for Middle Censoring

Usage

loglik_middle(theta, data, pdf, cdf, survival, scheme_params = NULL)

Arguments

Value

Log-likelihood value.

Log-Likelihood for Progressive First Failure Censoring

Description

Log-Likelihood for Progressive First Failure Censoring

Usage

loglik_progressive_first_failure(
  theta,
  data,
  pdf,
  cdf,
  survival,
  scheme_params = NULL
)

Arguments

Value

Log-likelihood value.

Log-Likelihood for Progressive Type-II Censoring

Description

Log-Likelihood for Progressive Type-II Censoring

Usage

loglik_progressive_type2(theta, data, pdf, cdf, survival, scheme_params = NULL)

Arguments

Value

Log-likelihood value.

Log-Likelihood for Random Censoring

Description

Log-Likelihood for Random Censoring

Usage

loglik_random(theta, data, pdf, cdf, survival, scheme_params = NULL)

Arguments

Value

Log-likelihood value.

Log-Likelihood for Right Censoring

Description

Log-Likelihood for Right Censoring

Usage

loglik_right(theta, data, pdf, cdf, survival, scheme_params = NULL)

Arguments

Value

Log-likelihood value.

Log-Likelihood for Right Truncation

Description

Log-Likelihood for Right Truncation

Usage

loglik_right_truncation(theta, data, pdf, cdf, survival, scheme_params = NULL)

Arguments

Value

Log-likelihood value.

Log-Likelihood for Type-I Censoring

Description

Log-Likelihood for Type-I Censoring

Usage

loglik_type1(theta, data, pdf, cdf, survival, scheme_params = NULL)

Arguments

Value

Log-likelihood value.

Log-Likelihood for Type-I Hybrid Censoring

Description

Log-Likelihood for Type-I Hybrid Censoring

Usage

loglik_type1_hybrid(theta, data, pdf, cdf, survival, scheme_params = NULL)

Arguments

Value

Log-likelihood value.

Log-Likelihood for Type-II Censoring

Description

Log-Likelihood for Type-II Censoring

Usage

loglik_type2(theta, data, pdf, cdf, survival, scheme_params = NULL)

Arguments

Value

Log-likelihood value.

Log-Likelihood for Type-II Progressively Hybrid Censoring

Description

Log-Likelihood for Type-II Progressively Hybrid Censoring

Usage

loglik_type2_progressively_hybrid(
  theta,
  data,
  pdf,
  cdf,
  survival,
  scheme_params = NULL
)

Arguments

Value

Log-likelihood value.

Loss Functions for Bayesian Estimation

Description

Implements various loss functions for computing Bayes estimates.

Usage

loss_self(theta, estimate, ...)

loss_wself(theta, estimate, w = 1, ...)

loss_mqself(theta, estimate, k = 1, ...)

loss_plf(theta, estimate, a = 1, ...)

loss_elf(theta, estimate, ...)

loss_linex(theta, estimate, a = 1, ...)

loss_gelf(theta, estimate, q = 2, ...)

loss_kloss(theta, estimate, ...)

Arguments

Value

Loss value.

Loss value: (theta - estimate)^2

Loss value: w * (theta - estimate)^2

Loss value: (theta - estimate)^2 / (k + theta^2)

Loss value: (estimate/theta)^a - a * log(estimate/theta) - 1

Loss value: estimate/theta - log(estimate/theta) - 1

Loss value: exp(a * (estimate - theta)) - a * (estimate - theta) - 1

Loss value: (estimate/theta)^q / q - (estimate/theta) + 1/q

Loss value: (theta - estimate)^2 / (theta * estimate)

Mean Absolute Error

Description

Computes mean absolute error between observed and fitted quantities.

Usage

mae(fit, type = "density", ...)

Arguments

Value

MAE value.

Mean Squared Error

Description

Computes mean squared error between observed and fitted quantities.

Usage

mse(fit, type = "density", ...)

Arguments

Value

MSE value.

Number of Observations for lindleyfit Objects

Description

Number of Observations for lindleyfit Objects

Usage

nobs_lindleyfit(object)

Arguments

Value

Number of observations.

Numerical Integration

Description

Performs numerical integration using adaptive quadrature.

Usage

numerical_integrate(fun, lower, upper, ...)

Arguments

Value

Integration result.

BFGS Optimization

Description

BFGS Optimization

Usage

optim_bfgs(neg_logpost, theta0, control)

Brent Optimization (1D only)

Description

Brent Optimization (1D only)

Usage

optim_brent(neg_logpost, theta0, control)

Conjugate Gradient Optimization

Description

Conjugate Gradient Optimization

Usage

optim_cg(neg_logpost, theta0, control)

L-BFGS-B Optimization

Description

L-BFGS-B Optimization

Usage

optim_lbfgsb(neg_logpost, theta0, control)

Newton-Raphson Optimization

Description

Newton-Raphson Optimization

Usage

optim_newton(neg_logpost, theta0, control)

Nelder-Mead Optimization

Description

Nelder-Mead Optimization

Usage

optim_nm(neg_logpost, theta0, control)

Simulated Annealing Optimization

Description

Simulated Annealing Optimization

Usage

optim_sann(neg_logpost, theta0, control)

Optimize Function

Description

Optimizes a function using numerical methods.

Usage

optimize_fun(fun, par, method = "BFGS", ...)

Arguments

Value

Optimization result.

Plot Method for lindleyfit Objects

Description

Creates diagnostic plots for the fitted model.

Usage

## S3 method for class 'lindleyfit'
plot(x, which = 1:4, ask = TRUE, ...)

Arguments

Value

Invisibly returns the object.

Plot Fitted Distribution

Description

Plots the fitted distribution over the data histogram.

Usage

plot_fitted(fit, type = "density", n = 100, ...)

Arguments

Value

Invisibly returns the fitted values.

Plot Likelihood Surface

Description

Creates a contour or surface plot of the likelihood function.

Usage

plot_likelihood_surface(
  fit,
  theta1_range = NULL,
  theta2_range = NULL,
  n = 50,
  type = "contour",
  ...
)

Arguments

Value

Invisibly returns the grid of likelihood values.

Plot Posterior Surface

Description

Creates a contour or surface plot of the posterior distribution.

Usage

plot_posterior_surface(
  fit,
  theta1_range = NULL,
  theta2_range = NULL,
  n = 50,
  type = "contour",
  ...
)

Arguments

Value

Invisibly returns the grid of posterior values.

Plot Prior vs Posterior

Description

Compares prior and posterior distributions.

Usage

plot_prior_posterior(fit, param_range = NULL, n = 100, ...)

Arguments

Value

Invisibly returns the comparison data.

Plot Log-Likelihood Profile

Description

Creates a profile log-likelihood plot for each parameter.

Usage

plot_profile(fit, param_range = NULL, n = 50, ...)

Arguments

Value

Invisibly returns the profile data.

Plot Residuals

Description

Creates various residual plots.

Usage

plot_residuals(fit, type = "cox_snell", which = 1:3, ...)

Arguments

Value

Invisibly returns the residual values.

Visualization Functions for UniLindleyApprox

Description

Functions for creating diagnostic and exploratory plots.

Compute Posterior Expectation of Arbitrary Function

Description

General function to compute E[g(theta)|data] using Lindley's approximation.

Usage

posterior_expectation(fit, g_fun, ...)

Arguments

Value

Posterior expectation approximation.

Compute Posterior Mean Approximation

Description

Compute Posterior Mean Approximation

Usage

posterior_mean(fit, ...)

Arguments

Value

Posterior mean approximation.

Compute Posterior Median Approximation

Description

Approximates posterior median using Lindley's approximation. Note: This is an approximation and may not be accurate for all distributions.

Usage

posterior_median(fit, ...)

Arguments

Value

Posterior median approximation.

Predict Method for lindleyfit Objects

Description

Makes predictions for new data.

Usage

## S3 method for class 'lindleyfit'
predict(object, newdata = NULL, type = "density", ...)

Arguments

Value

Predicted values.

Predict Cumulative Hazard

Description

Predicts cumulative hazard values at specified time points.

Usage

predict_cumhaz(fit, times, ...)

Arguments

Value

Vector of cumulative hazard values.

Predict Failure Probability

Description

Predicts the probability of failure by a specified time.

Usage

predict_failure_prob(fit, t, ...)

Arguments

Value

Failure probability.

Predict Hazard Function

Description

Predicts hazard function values at specified time points.

Usage

predict_hazard(fit, times, ...)

Arguments

Value

Vector of hazard values.

Prediction Intervals (Based on Quantiles)

Description

Computes prediction intervals based on distribution quantiles. Note: This is a prediction interval for future observations, not a confidence interval for parameters (which is outside the scope of Lindley's approximation).

Usage

predict_interval(fit, level = 0.95, ...)

Arguments

Value

Vector with lower and upper bounds.

Predict Median Time to Failure

Description

Predicts the median time to failure from the fitted distribution.

Usage

predict_median(fit, ...)

Arguments

Value

Predicted median time to failure.

Predict Mean Time to Failure

Description

Predicts the mean time to failure from the fitted distribution.

Usage

predict_mttf(fit, ...)

Arguments

Value

Predicted mean time to failure.

Predict for New Data

Description

Makes predictions for new data points.

Usage

predict_new(fit, newdata, type = "density", ...)

Arguments

Value

Predicted values.

Predict Quantiles

Description

Predicts quantiles of the fitted distribution.

Usage

predict_quantiles(fit, probs = c(0.25, 0.5, 0.75), ...)

Arguments

Value

Vector of predicted quantiles.

Predict Remaining Lifetime

Description

Predicts the remaining lifetime distribution for a surviving unit.

Usage

predict_remaining_lifetime(fit, current_age, ...)

Arguments

Value

List with mean and median remaining lifetime.

Predict Survival Probabilities

Description

Predicts survival probabilities at specified time points.

Usage

predict_survival(fit, times, ...)

Arguments

Value

Vector of survival probabilities.

Predict Probability of Survival to Time T

Description

Predicts the probability of surviving to a specified time.

Usage

predict_survival_prob(fit, t, ...)

Arguments

Value

Survival probability.

Prediction Functions for UniLindleyApprox

Description

Functions for making predictions from fitted models.

Prediction Summary

Description

Provides a summary of prediction performance.

Usage

prediction_summary(fit, test_data, type = "density")

Arguments

Value

List with prediction performance metrics.

Print Method for lindleyfit Objects

Description

Print Method for lindleyfit Objects

Usage

## S3 method for class 'lindleyfit'
print(x, ...)

Arguments

Value

Invisibly returns the object.

Progress Bar

Description

Displays a simple progress bar.

Usage

progress_bar(current, total, prefix = "Progress:")

Arguments

Residuals Method for lindleyfit Objects

Description

Computes residuals for the fitted model.

Usage

## S3 method for class 'lindleyfit'
residuals(object, type = "cox_snell", ...)

Arguments

Value

Residual values.

Root Mean Squared Error

Description

Computes root mean squared error between observed and fitted quantities.

Usage

rmse(fit, type = "density", ...)

Arguments

Value

RMSE value.

Round to Significant Digits

Description

Rounds a number to specified significant digits.

Usage

round_sig(x, digits = 3)

Arguments

Value

Rounded value.

Safe Division

Description

Computes numerator/denominator with protection against division by zero.

Usage

safe_divide(numerator, denominator, eps = 1e-10)

Arguments

Value

Division result.

Safe Logarithm

Description

Computes log(x) with protection against non-positive values.

Usage

safe_log(x, eps = 1e-10)

Arguments

Value

Logarithm value.

Simulate Complete Data

Description

Generates complete (uncensored) random samples from a specified distribution.

Usage

simulate_complete(n, pdf, cdf, theta, ...)

Arguments

Value

Vector of simulated observations.

Simulate Hybrid Censored Data

Description

Generates hybrid censored random samples.

Usage

simulate_hybrid(n, pdf, cdf, survival, theta, censoring_time, r, ...)

Arguments

Value

List with observed data and censoring information.

Simulate Interval Censored Data

Description

Generates interval censored random samples.

Usage

simulate_interval(n, pdf, cdf, survival, theta, interval_width, ...)

Arguments

Value

Matrix with lower and upper bounds.

Simulate Left Censored Data

Description

Generates left censored random samples.

Usage

simulate_left(n, pdf, cdf, survival, theta, censoring_time, ...)

Arguments

Value

List with observed and censored components.

Simulate Left Truncated Data

Description

Generates left truncated random samples.

Usage

simulate_left_truncation(n, pdf, cdf, survival, theta, truncation_point, ...)

Arguments

Value

List with observed data and truncation information.

Simulate Middle Censored Data

Description

Generates middle censored random samples.

Usage

simulate_middle(n, pdf, cdf, survival, theta, left_bound, right_bound, ...)

Arguments

Value

List with observed data and censoring information.

Simulate Progressive Type-II Censored Data

Description

Generates progressive Type-II censored random samples.

Usage

simulate_progressive(n, pdf, cdf, survival, theta, m, removal_scheme, ...)

Arguments

Value

List with observed data and censoring information.

Simulate Random Censored Data

Description

Generates random censored random samples.

Usage

simulate_random(
  n,
  pdf,
  cdf,
  survival,
  theta,
  censoring_dist = "exp",
  censoring_params = list(rate = 0.5),
  ...
)

Arguments

Value

List with observed data and censoring information.

Simulate Right Censored Data

Description

Generates right censored random samples.

Usage

simulate_right(n, pdf, cdf, survival, theta, censoring_time, ...)

Arguments

Value

List with observed and censored components.

Simulate Right Truncated Data

Description

Generates right truncated random samples.

Usage

simulate_right_truncation(n, pdf, cdf, survival, theta, truncation_point, ...)

Arguments

Value

List with observed data and truncation information.

Simulate Type-I Censored Data

Description

Generates Type-I censored random samples.

Usage

simulate_type1(n, pdf, cdf, survival, theta, censoring_time, ...)

Arguments

Value

List with observed data and censoring information.

Simulate Type-II Censored Data

Description

Generates Type-II censored random samples.

Usage

simulate_type2(n, pdf, cdf, survival, theta, r, ...)

Arguments

Value

List with observed order statistics and censoring information.

Simulation Utilities for Censoring Schemes

Description

Functions to generate simulated data under various censoring schemes for benchmarking Bayesian estimators.

Simulation Study for Bayesian Estimators

Description

Performs a simulation study to evaluate Bayesian estimators under repeated sampling.

Usage

simulation_study(
  nsim,
  n,
  pdf,
  cdf,
  survival,
  log_prior,
  theta_true,
  theta0,
  scheme = "complete",
  scheme_params = NULL,
  loss = "SELF",
  control = lindley.control(verbose = FALSE),
  parallel = FALSE,
  ncores = 2,
  ...
)

Arguments

Value

Data frame with simulation results.

Softmax Function

Description

Computes the softmax of a vector.

Usage

softmax(x)

Arguments

Value

Softmax values.

Summary Method for lindleyfit Objects

Description

Summary Method for lindleyfit Objects

Usage

## S3 method for class 'lindleyfit'
summary(object, ...)

Arguments

Value

A list with summary statistics.

Timer

Description

Simple timer for benchmarking.

Usage

timer()

Utility Functions for UniLindleyApprox

Description

Various helper functions used throughout the package.

Validate Data Format

Description

Validate Data Format

Usage

validate_data_format(data, scheme)

Validate Function

Description

Validates that input is a function.

Usage

validate_function(x, name = "x")

Arguments

Value

TRUE if valid, otherwise stops with error.

Validate Inputs for Lindley Fit

Description

Validate Inputs for Lindley Fit

Usage

validate_inputs(data, pdf, cdf, survival, log_prior, theta0, scheme, control)

Validate Numeric Vector

Description

Validates that input is a numeric vector.

Usage

validate_numeric(x, name = "x")

Arguments

Value

TRUE if valid, otherwise stops with error.

Validate Positive

Description

Validates that numeric values are positive.

Usage

validate_positive(x, name = "x")

Arguments

Value

TRUE if valid, otherwise stops with error.

Validate Prior Function

Description

Checks if a prior function is valid.

Usage

validate_prior(log_prior, theta, ...)

Arguments

Value

Logical indicating validity.

Validate Probability

Description

Validates that values are in [0, 1].

Usage

validate_probability(x, name = "x")

Arguments

Value

TRUE if valid, otherwise stops with error.

Print Warning if Not Converged

Description

Prints a warning if optimization did not converge.

Usage

warn_if_not_converged(convergence, method)

Arguments