Package {UniIS}

Type: Package
Title: Importance Sampling Inference for Censored Univariate Data
Version: 0.1.0
Description: Distribution-independent framework for importance-sampling inference with univariate observations subject to censoring or truncation. Users provide probability functions and a proposal over model parameters. Constructs observed-data likelihood contributions, computes numerically stable importance weights, and supplies posterior, likelihood, predictive, diagnostic, and model-comparison summaries. Covers complete, right, left, interval, Type-I, Type-II, progressive Type-II, first-failure, progressive first-failure, doubly Type-II, middle-censored, and left/right-truncated data. Methods for importance sampling and censoring schemes are described in Geweke (1989) <doi:10.2307/2290062>, Hesterberg (1995) <doi:10.1080/00031305.1995.10476138>, Robert and Casella (2004, ISBN:978-0-387-21617-1), Kundu and Joarder (2006) <doi:10.1016/j.csda.2005.05.002>, Banerjee and Kundu (2008) <doi:10.1109/TR.2008.916890>, Iyer, Jammalamadaka, and Kundu (2008) <doi:10.1016/j.jspi.2007.03.062>, Wu and Kus (2009) <doi:10.1016/j.csda.2009.03.010>, Prajapati, Mitra, and Kundu (2019) <doi:10.1007/s13571-018-0167-0>, Mondal and Kundu (2020) <doi:10.1080/03610926.2018.1554128>, Balakrishnan and Aggarwala (2000, ISBN:980-1-4612-1334-5), Ding and Gui (2023) <doi:10.3390/math11092003>, Nagar, Kumar, and Krishna (2026) <doi:10.59467/IJASS.2026.22.1>, Goel and Krishna (2026) <doi:10.1007/s13198-026-03208-w>, Yadav, Jaiswal, and Yadav (2026) <doi:10.1007/s11135-026-02647-8>, and Goel, Kumar, and Krishna (2026, "Estimation in power Lindley distributions using balanced joint progressively Type-II censored data").
License: GPL-3
Encoding: UTF-8
Language: en-US
Depends: R (≥ 4.1.0)
Imports: stats, graphics
Suggests: testthat (≥ 3.0.0), knitr, rmarkdown
Config/testthat/edition: 3
RoxygenNote: 7.3.3
VignetteBuilder: knitr
NeedsCompilation: no
Packaged: 2026-07-28 16:14:41 UTC; shikhar tyagi
Author: Shikhar Tyagi ORCID iD [aut, cre], Arvind Pandey [aut], Bhupendra Singh [aut], Vrijesh Tripathi [aut]
Maintainer: Shikhar Tyagi <shikhar1093tyagi@gmail.com>
Repository: CRAN
Date/Publication: 2026-08-06 10:10:02 UTC

UniIS: Importance Sampling for Censored Univariate Data

Description

UniIS performs distribution-independent importance-sampling inference for univariate data under common censoring and truncation mechanisms. Start with is_fit() and use is_dist() to keep a distribution specification reusable.

Author(s)

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

Authors:

References

Balakrishnan, N., & Aggarwala, R. (2000). Progressive Censoring: Theory, Methods, and Applications. Birkhauser. ISBN: 978-1-4612-1334-5.

Banerjee, A., & Kundu, D. (2008). Inference based on Type-II hybrid censored data from Weibull distribution. IEEE Transactions on Reliability, 57(2), 369-378. doi:10.1109/TR.2008.916890

Ding, C., & Gui, W. (2023). Statistical inference of power Lindley distribution under progressive first-failure censoring. Mathematics, 11(9), 2003. doi:10.3390/math11092003

Geweke, J. (1989). Bayesian inference in econometric models using Monte Carlo integration. Econometrica, 57(6), 1317-1339. doi:10.2307/2290062

Goel, C., & Krishna, H. (2026). Reliability estimation in inverse Weibull distribution under progressive Type-II censoring. Journal of Reliability and Statistical Studies. doi:10.1007/s13198-026-03208-w

Goel, C., Kumar, M., & Krishna, H. (2026). Estimation in power Lindley distributions using balanced joint progressively Type-II censored data. Preprint.

Hesterberg, T. (1995). Weighted average importance sampling and defensive mixture distributions. Technometrics, 37(2), 185-194. doi:10.1080/00031305.1995.10476138

Iyer, S. K., Jammalamadaka, S. R., & Kundu, D. (2008). Analysis of middle-censored data with exponential lifetime distribution. Journal of Statistical Planning and Inference, 138(11), 3550-3560. doi:10.1016/j.jspi.2007.03.062

Kundu, D., & Joarder, A. (2006). Analysis of Type-II progressively hybrid censored data. Computational Statistics & Data Analysis, 50(10), 2509-2528. doi:10.1016/j.csda.2005.05.002

Mondal, S., & Kundu, D. (2020). Point and interval estimation of parameters of Weibull distribution under middle censoring scheme. Communications in Statistics - Theory and Methods, 49(8), 1984-2003. doi:10.1080/03610926.2018.1554128

Nagar, S., Kumar, M., & Krishna, H. (2026). Bayesian estimation under censoring. International Journal of Agricultural and Statistical Sciences, 22(1). doi:10.59467/IJASS.2026.22.1

Prajapati, A., Mitra, S., & Kundu, D. (2019). On progressive first-failure censoring scheme. Journal of Statistical Theory and Practice, 13(1), 16. doi:10.1007/s13571-018-0167-0

Robert, C. P., & Casella, G. (2004). Monte Carlo Statistical Methods (2nd ed.). Springer. ISBN: 978-0-387-21617-1.

Wu, S. J., & Kus, C. (2009). On estimation methods for the Weibull distribution under progressive first-failure censored data. Computational Statistics & Data Analysis, 53(10), 3617-3626. doi:10.1016/j.csda.2009.03.010

Yadav, A. S., Jaiswal, S., & Yadav, S. K. (2026). Statistical properties and inference for censoring schemes. Quality & Quantity. doi:10.1007/s11135-026-02647-8

Build an observed-data likelihood specification

Description

Internal parsers use a small common representation: exact observations, interval probabilities, and conditioning regions for truncation. A custom scheme function may return that representation, enabling new schemes without changing the importance-sampling engine.

Usage

.is_observations(
  data,
  scheme = "complete",
  status = NULL,
  time2 = NULL,
  censor_params = list()
)

Arguments

data

observed data.

scheme

censoring scheme name, or a parser function.

status

event indicator; 1 denotes an exact event.

time2

upper interval endpoints.

censor_params

scheme-specific values such as censor_time, n, R, or k.

Value

A list used internally by is_loglik().

Control settings for importance sampling

Description

Control settings for importance sampling

Usage

is_control(
  n_draws = 10000L,
  method = c("self_normalized", "ordinary", "adaptive"),
  adapt_fraction = 0.25,
  min_ess = 50,
  truncate_weights = Inf,
  seed = NULL,
  optimize = TRUE,
  optim_control = list()
)

Arguments

n_draws

number of parameter draws.

method

one of "self_normalized", "ordinary", or "adaptive".

adapt_fraction

pilot fraction for adaptive deterministic-mixture IS.

min_ess

minimum ESS required before a warning is issued.

truncate_weights

optional positive cap on normalized weights, as a multiple of 1 / n_draws; use Inf to disable truncation.

seed

optional integer seed.

optimize

whether to refine the maximum-likelihood draw using optim.

optim_control

control list passed to optim.

Value

A list of class is_control.

Importance-sampling diagnostics

Description

Importance-sampling diagnostics

Usage

is_diagnostics(object)

Arguments

object

an isfit object.

Value

A list containing ESS, weight dispersion, entropy, and Monte Carlo standard errors for parameter means.

Define a distribution specification

Description

Define a distribution specification

Usage

is_dist(
  pdf,
  cdf = NULL,
  survival = NULL,
  support = c(-Inf, Inf),
  name = "custom"
)

Arguments

pdf

function of x and theta returning a density.

cdf

optional function of x and theta returning a CDF.

survival

optional survival function of x and theta.

support

numeric length-two support bounds for the observations.

name

descriptive label.

Value

An object of class is_dist.

Fit a censored univariate model by importance sampling

Description

is_fit() samples parameter values from a proposal distribution, evaluates the observed-data likelihood for each draw, and computes stable normalized importance weights. With prior (or log_prior) it returns a Bayesian posterior approximation; without one, it approximates the normalized likelihood under a flat reference measure. The reported par is an observed likelihood maximum refined from the best importance draw when requested.

Usage

is_fit(
  data,
  pdf,
  cdf = NULL,
  survival = NULL,
  theta0,
  proposal = NULL,
  proposal_density = NULL,
  prior = NULL,
  log_prior = NULL,
  support = c(-Inf, Inf),
  scheme = "complete",
  status = NULL,
  time2 = NULL,
  censor_params = list(),
  control = is_control()
)

Arguments

data

observed data, a numeric vector, data frame, or list.

pdf

density function pdf(x, theta).

cdf

CDF function cdf(x, theta).

survival

survival function survival(x, theta).

theta0

initial parameter vector, used to validate dimension and make a default normal proposal when proposal is omitted.

proposal

proposal object, or a function proposal(n).

proposal_density

density function for a function-valued proposal.

prior

prior density prior(theta).

log_prior

log prior function log_prior(theta).

support

observation support bounds retained in the fitted object.

scheme

censoring or truncation scheme.

status

event status indicator.

time2

upper interval endpoints.

censor_params

scheme-specific parameters.

control

settings from is_control().

Value

An object of class isfit.

References

Geweke, J. (1989). Bayesian inference in econometric models using Monte Carlo integration. Econometrica, 57(6), 1317-1339. doi:10.2307/2290062

Hesterberg, T. (1995). Weighted average importance sampling and defensive mixture distributions. Technometrics, 37(2), 185-194. doi:10.1080/00031305.1995.10476138

Robert, C. P., & Casella, G. (2004). Monte Carlo Statistical Methods (2nd ed.). Springer. ISBN: 978-0-387-21617-1.

Examples

x <- rexp(40, 1.5)
proposal <- is_proposal_normal(log(1.5), 0.5)
fit <- is_fit(x,
  pdf = function(x, theta) dexp(x, rate = exp(theta[1])),
  cdf = function(x, theta) pexp(x, rate = exp(theta[1])),
  survival = function(x, theta) pexp(x, rate = exp(theta[1]), lower.tail = FALSE),
  theta0 = log(1), proposal = proposal, scheme = "complete",
  control = is_control(n_draws = 500)
)
exp(coef(fit))

Observed-data log likelihood

Description

Computes a log likelihood for an arbitrary univariate distribution. The density, CDF, and survival functions all use the convention fun(x, theta).

Usage

is_loglik(
  data,
  theta,
  pdf,
  cdf = NULL,
  survival = NULL,
  scheme = "complete",
  status = NULL,
  time2 = NULL,
  censor_params = list()
)

Arguments

data

observed data.

theta

numeric parameter vector.

pdf

density function.

cdf

CDF function; required for finite or left-censored intervals.

survival

survival function; an alternative to cdf for right tails.

scheme

censoring/truncation scheme.

status

event status.

time2

interval upper endpoints.

censor_params

additional scheme parameters.

Value

A scalar log likelihood.

References

Balakrishnan, N., & Aggarwala, R. (2000). Progressive Censoring: Theory, Methods, and Applications. Birkhauser. ISBN: 978-1-4612-1334-5.

Banerjee, A., & Kundu, D. (2008). Inference based on Type-II hybrid censored data from Weibull distribution. IEEE Transactions on Reliability, 57(2), 369-378. doi:10.1109/TR.2008.916890

Ding, C., & Gui, W. (2023). Statistical inference of power Lindley distribution under progressive first-failure censoring. Mathematics, 11(9), 2003. doi:10.3390/math11092003

Goel, C., & Krishna, H. (2026). Reliability estimation in inverse Weibull distribution under progressive Type-II censoring. Journal of Reliability and Statistical Studies. doi:10.1007/s13198-026-03208-w

Goel, C., Kumar, M., & Krishna, H. (2026). Estimation in power Lindley distributions using balanced joint progressively Type-II censored data. Preprint.

Iyer, S. K., Jammalamadaka, S. R., & Kundu, D. (2008). Analysis of middle-censored data with exponential lifetime distribution. Journal of Statistical Planning and Inference, 138(11), 3550-3560. doi:10.1016/j.jspi.2007.03.062

Kundu, D., & Joarder, A. (2006). Analysis of Type-II progressively hybrid censored data. Computational Statistics & Data Analysis, 50(10), 2509-2528. doi:10.1016/j.csda.2005.05.002

Mondal, S., & Kundu, D. (2020). Point and interval estimation of parameters of Weibull distribution under middle censoring scheme. Communications in Statistics - Theory and Methods, 49(8), 1984-2003. doi:10.1080/03610926.2018.1554128

Nagar, S., Kumar, M., & Krishna, H. (2026). Bayesian estimation under censoring. International Journal of Agricultural and Statistical Sciences, 22(1). doi:10.59467/IJASS.2026.22.1

Prajapati, A., Mitra, S., & Kundu, D. (2019). On progressive first-failure censoring scheme. Journal of Statistical Theory and Practice, 13(1), 16. doi:10.1007/s13571-018-0167-0

Wu, S. J., & Kus, C. (2009). On estimation methods for the Weibull distribution under progressive first-failure censored data. Computational Statistics & Data Analysis, 53(10), 3617-3626. doi:10.1016/j.csda.2009.03.010

Yadav, A. S., Jaiswal, S., & Yadav, S. K. (2026). Statistical properties and inference for censoring schemes. Quality & Quantity. doi:10.1007/s11135-026-02647-8

Model comparison for multiple IS fits

Description

Model comparison for multiple IS fits

Usage

is_model_comparison(...)

Arguments

...

one or more isfit objects.

Value

A data frame comparing logLik, AIC, AICc, BIC, CAIC, and HQIC.

Compute an expectation from an IS fit

Description

Compute an expectation from an IS fit

Usage

is_posterior_expectation(object, fun)

Arguments

object

an isfit object.

fun

function mapping one parameter vector to a numeric scalar or fixed-length numeric vector.

Value

Weighted posterior or normalized-likelihood expectation.

Posterior predictive functionals

Description

Posterior predictive functionals

Usage

is_predictive(object, x, type = c("density", "cdf", "survival"))

Arguments

object

an isfit object.

x

values at which to evaluate the predictive quantity.

type

"density", "cdf", or "survival".

Value

A weighted predictive estimate at x.

Defensive mixture proposal

Description

Constructs a deterministic mixture of two proposals. The defensive component protects against under-dispersed initial proposals and is evaluated exactly in the resulting mixture density.

Usage

is_proposal_defensive(primary, defensive, epsilon = 0.1)

Arguments

primary

proposal object.

defensive

proposal object of the same dimension.

epsilon

mixture weight assigned to the defensive proposal.

Value

A proposal object accepted by is_fit().

Multivariate normal proposal for model parameters

Description

This base-R proposal is convenient for unconstrained parameters. For constrained parameters, provide a proposal on a suitable transformed scale and incorporate the Jacobian in proposal_density.

Usage

is_proposal_normal(mean, covariance)

Arguments

mean

proposal mean.

covariance

positive-definite covariance matrix, or positive variances.

Value

A proposal object accepted by is_fit().

Student t proposal for model parameters

Description

Student t proposal for model parameters

Usage

is_proposal_t(mean, scale, df = 4)

Arguments

mean

proposal location.

scale

positive-definite scale matrix or variances.

df

degrees of freedom.

Value

A proposal object accepted by is_fit().

Uniform proposal for model parameters

Description

Uniform proposal for model parameters

Usage

is_proposal_uniform(lower, upper)

Arguments

lower

lower bounds for parameters.

upper

upper bounds for parameters.

Value

A proposal object accepted by is_fit().

Simulate complete univariate data

Description

Simulate complete univariate data

Usage

simulate_complete(n, rfun, theta)

Arguments

n

sample size.

rfun

random-generation function rfun(n, theta).

theta

parameter vector passed to rfun.

Value

A numeric sample.

Simulate hybrid-censored data

Description

Simulate hybrid-censored data

Usage

simulate_hybrid(n, rfun, theta, censor_time, m = NULL)

Arguments

n

initial sample size.

rfun

random-generation function rfun(n, theta).

theta

model parameters.

censor_time

fixed censoring time.

m

target failure count (1 <= m <= n).

Value

A data frame with x and event status.

Simulate interval-censored data

Description

Simulate interval-censored data

Usage

simulate_interval(n, rfun, theta, inspection_times)

Arguments

n

sample size.

rfun

random-generation function rfun(n, theta).

theta

model parameters.

inspection_times

strictly increasing finite inspection times.

Value

A data frame with interval endpoints L and R.

Simulate left-censored data

Description

Simulate left-censored data

Usage

simulate_left(n, rfun, theta, censoring)

Arguments

n

sample size.

rfun

random-generation function rfun(n, theta).

theta

model parameters.

censoring

either one censoring time or a function censoring(n).

Value

A data frame with x and event status.

Simulate progressively Type-II-censored data

Description

Simulate progressively Type-II-censored data

Usage

simulate_progressive(rfun, theta, R)

Arguments

rfun

random-generation function rfun(n, theta).

theta

model parameters.

R

non-negative removals immediately after successive observed failures.

Value

A list suitable for scheme = "progressive_type2".

Simulate right-censored data

Description

Simulate right-censored data

Usage

simulate_right(n, rfun, theta, censoring)

Arguments

n

sample size.

rfun

random-generation function rfun(n, theta).

theta

model parameters.

censoring

either one censoring time or a function censoring(n).

Value

A data frame with x and event status.

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