Help for package TieFreeCensor

Type:

Package

Title:

Algorithm for Generating Tie-Free Progressive Type-II Censored Samples

Version:

0.1.0

Description:

Generates tie-free progressive Type-II censored samples from discrete distributions and user-specified discrete probability mass functions (PMF) or cumulative distribution functions (CDF). Provides maximum likelihood estimation (MLE), Bayesian estimation via Markov chain Monte Carlo (MCMC) Metropolis-within-Gibbs sampling, likelihood-based parametric bootstrap goodness-of-fit (GOF) tests, profile log-likelihood diagnostics, and discrete survival and probability calculations. Methods are based on Ahmad and Mansour (2026) <doi:10.1155/jom/3657078>, Balakrishnan and Dembinska (2008) <doi:10.1016/j.jspi.2007.02.006>, Joe and Zhu (2005) <doi:10.1002/bimj.200410102>, and Balakrishnan and Aggarwala (2000, ISBN:978-1-4612-1334-5).

License:

GPL (≥ 3)

Encoding:

UTF-8

LazyData:

true

Depends:

R (≥ 4.0.0)

Imports:

stats, graphics

Suggests:

testthat (≥ 3.0.0)

Config/testthat/edition:

RoxygenNote:

7.3.3

NeedsCompilation:

Packaged:

2026-08-05 19:52:59 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:

2026-08-21 12:41:06 UTC

Coef Method for GPD MLE

Description

Coef Method for GPD MLE

Usage

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

Arguments

object

Object of class "gpd_mle".

...

Additional arguments.

Value

A named numeric vector of length 2 containing the maximum likelihood estimates for parameters q (mean parameter) and h (dispersion parameter).

COVID-19 Daily Death Counts Dataset

Description

Dataset containing 25 daily COVID-19 death counts recorded in the US Virgin Islands during May 2021, as reported by Worldometer (2021) and analyzed by Ahmad and Mansour (2026).

Usage

covid_deaths

Format

A numeric vector of length 25 containing daily reported death counts.

Source

Worldometer (2021). COVID-19 Coronavirus Pandemic.

References

Ahmad, H. H., & Mansour, M. M. M. (2026). An Algorithm for Generating Tie-Free Progressive Type-II Censored Samples From Discrete Distributions. Journal of Mathematics, 2026, 3657078.

Bayesian Estimation for GPD Under Progressive Type-II Censoring

Description

Fits the Generalized Poisson Distribution (GPD) to a tie-free progressively Type-II right-censored sample using Bayesian Markov chain Monte Carlo (MCMC) with Metropolis-within-Gibbs sampling on transformed parameters.

Usage

fit_gpd_bayes(
  x,
  R,
  hyper_a = 1,
  hyper_b = 1,
  hyper_c = 10,
  iter = 5000,
  burnin = 1000,
  thin = 1,
  start = NULL,
  prop_sd = c(0.05, 0.05),
  conf_level = 0.95
)

Arguments

x

Numeric vector of observed tie-free failure times (x_1 < x_2 < \dots < x_m).

R

Numeric vector of progressive removal counts (R_1, R_2, \dots, R_m).

hyper_a

Shape parameter a > 0 for Beta prior on h. Default is 1 (Uniform).

hyper_b

Shape parameter b > 0 for Beta prior on h. Default is 1 (Uniform).

hyper_c

Scale parameter c > 0 for Exponential prior on q. Default is 10.

iter

Total number of MCMC iterations. Default is 5000.

burnin

Number of initial iterations discarded as burn-in. Default is 1000.

thin

Thinning interval. Default is 1.

start

Numeric vector of length 2 giving starting values c(q, h). If NULL, defaults to sample estimates.

prop_sd

Numeric vector of length 2 specifying proposal standard deviations for (\log q, \text{logit } h). Default is c(0.05, 0.05).

conf_level

Credible level for equal-tailed credible intervals (CRI). Default is 0.95.

Value

A list of class "gpd_bayes" containing:

estimates: Vector of posterior means (SEL) for q and h.
sd: Posterior standard deviations.
cri: Matrix of equal-tailed credible intervals (2.5% and 97.5% quantiles).
draws: Matrix of thinned MCMC posterior samples for q and h.
accept_rates: Acceptance rates for MCMC updates.
data: List containing original input data.

References

Ahmad, H. H., & Mansour, M. M. M. (2026). An Algorithm for Generating Tie-Free Progressive Type-II Censored Samples From Discrete Distributions. Journal of Mathematics, 2026, 3657078. doi:10.1155/jom/3657078

Examples

# NF2 Spinal Tumors dataset example from paper
x_tumor <- c(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16)
R_tumor <- c(69, 12, 14, 5, 6, 4, 8, 8, 0, 1, 4, 0, 0, 0, 0, 11)
set.seed(123)
fit_b <- fit_gpd_bayes(x = x_tumor, R = R_tumor, iter = 2000, burnin = 500)
print(fit_b)
summary(fit_b)

Maximum Likelihood Estimation for GPD Under Progressive Type-II Censoring

Description

Fits the Generalized Poisson Distribution (GPD) to a tie-free progressively Type-II right-censored sample using Maximum Likelihood Estimation (MLE).

Usage

fit_gpd_mle(x, R, start = NULL, method = "BFGS", conf_level = 0.95, ...)

Arguments

x

Numeric vector of observed tie-free failure times (x_1 < x_2 < \dots < x_m).

R

Numeric vector of progressive removal counts (R_1, R_2, \dots, R_m).

start

Numeric vector of length 2 giving initial parameter values c(q, h). If NULL, starting values are calculated using sample moments.

method

Optimization method passed to optim. Options include "BFGS", "Nelder-Mead", "L-BFGS-B", "CG". Default is "BFGS".

conf_level

Confidence level for asymptotic confidence intervals (ACI). Default is 0.95.

...

Additional control parameters passed to optim.

Value

An object of class "gpd_mle" containing:

par: Vector of estimated parameters (\hat{q}, \hat{h}).
se: Vector of standard errors for \hat{q} and \hat{h}.
vcov: Estimated variance-covariance matrix.
loglik: Maximum log-likelihood value.
aci: Matrix of asymptotic confidence intervals.
convergence: Optimization convergence code.
data: List containing original data x and removal scheme R.

References

Examples

# NF2 Spinal Tumors dataset example from paper
x_tumor <- c(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16)
R_tumor <- c(69, 12, 14, 5, 6, 4, 8, 8, 0, 1, 4, 0, 0, 0, 0, 11)
fit_mle <- fit_gpd_mle(x = x_tumor, R = R_tumor)
print(fit_mle)
summary(fit_mle)

Generate Tie-Free Progressive Type-II Censored Samples

Description

Implements the constructive algorithm described by Ahmad and Mansour (2026) to generate progressively Type-II right-censored samples that are guaranteed to be free of ties, even when the underlying discrete distribution produces repeated values.

Usage

generate_tiefree_p2c(
  x0 = NULL,
  n = NULL,
  m = NULL,
  R = NULL,
  dist = c("gpd", "poisson", "geometric", "nbinom", "custom"),
  dist_pmf = NULL,
  dist_cdf = NULL,
  params = list(),
  max_attempts = 100
)

Arguments

x0

Numeric vector representing the original complete discrete dataset (with potential ties), or NULL if generating from a distribution.

n

Target total sample size (if generating from distribution). Defaults to length(x0).

m

Target number of observed failures. If NULL or larger than the maximum available distinct values, it is automatically adjusted.

R

Numeric vector specifying the progressive removal scheme (R_1, R_2, \dots, R_m) such that \sum R_i = n - m. If NULL, a default uniform or right-heavy scheme is generated.

dist

Character string specifying built-in discrete distribution if x0 is NULL. Options: "gpd" (Generalized Poisson), "poisson", "geometric", "nbinom".

dist_pmf

Custom function for discrete PMF P(X = x) taking quantiles as first argument. Used when x0 is NULL and dist = "custom".

dist_cdf

Custom function for discrete CDF P(X \le x) taking quantiles as first argument.

params

List of parameter values passed to distribution functions.

max_attempts

Maximum number of simulation attempts to find a tie-free sample before reducing candidate m.

Value

A list of class "tiefree_p2c" containing:

x

Numeric vector of tie-free observed progressive Type-II failure times (x_{(1)} < x_{(2)} < \dots < x_{(m)}).

R

Numeric vector of final progressive removal counts.

n

Total original sample size.

m

Final number of observed failure times.

x0

Original discrete dataset (with ties).

m_max

Number of distinct values in the original dataset.

References

Balakrishnan, N., & Dembińska, A. (2008). Progressively Type-II right censored order statistics from discrete distributions. Journal of Statistical Planning and Inference, 138(4), 845-856.

Examples

set.seed(123)
# Generate tie-free progressive Type-II sample from GPD
res <- generate_tiefree_p2c(n = 30, m = 15, dist = "gpd", params = list(q = 3.0, h = 0.3))
print(res)

# Generate tie-free sample from a raw dataset with ties
raw_data <- c(0,0,0,1,1,2,2,3,4,4,5,6,6,7,8,9,10)
res_raw <- generate_tiefree_p2c(x0 = raw_data, m = 8)
print(res_raw)

Likelihood-Based Parametric Bootstrap Goodness-of-Fit Test

Description

Evaluates model adequacy for progressively Type-II censored discrete data using a likelihood-based parametric bootstrap test, as formulated in Section 6.1 of Ahmad and Mansour (2026).

Usage

gof_p2c_bootstrap(x, R, B = 100, dist = "gpd", alpha = 0.05)

Arguments

x

Numeric vector of observed tie-free failure times (x_1 < x_2 < \dots < x_m).

R

Numeric vector of progressive removal counts (R_1, R_2, \dots, R_m).

B

Number of bootstrap replications. Default is 100.

dist

Model family under test. Default is "gpd".

alpha

Significance level for hypothesis testing. Default is 0.05.

Value

An object of class "gof_bootstrap" containing:

statistic: Observed test statistic T^{(obs)} = -2 \log L(\hat{q}, \hat{h}).
p_value: Monte Carlo bootstrap p-value.
mle: MLE fit object for the observed dataset.
bootstrap_stats: Vector of bootstrap test statistics T^{(b)} = -2 \log L(\hat{q}^{(b)}, \hat{h}^{(b)}).
B: Number of successful bootstrap replicates.
decision: Hypothesis test conclusion ("Fail to reject H0" or "Reject H0").

References

Besag, J., & Clifford, P. (1991). Sequential Monte Carlo p-values. Biometrika, 78(2), 301-304.

Examples


# NF2 Spinal Tumors dataset test
x_tumor <- c(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16)
R_tumor <- c(69, 12, 14, 5, 6, 4, 8, 8, 0, 1, 4, 0, 0, 0, 0, 11)
set.seed(123)
test_res <- gof_p2c_bootstrap(x = x_tumor, R = R_tumor, B = 20)
print(test_res)

Generalized Poisson Distribution Cumulative Distribution Function

Description

Evaluates the cumulative distribution function (CDF) of the Generalized Poisson Distribution (GPD).

Usage

gpd_cdf(x, q, h, lower_tail = TRUE, log_p = FALSE)

Arguments

x

Numeric vector of quantiles.

q

Parameter q > 0.

h

Parameter 0 \le h < 1.

lower_tail

Logical; if TRUE (default), probabilities are P(X \le x), otherwise P(X > x).

log_p

Logical; if TRUE, probabilities are given as \log(p). Default is FALSE.

Value

Numeric vector of CDF values.

Examples

gpd_cdf(x = 5, q = 3.0, h = 0.2)

Generalized Poisson Distribution (GPD) Probability Mass Function

Description

Evaluates the probability mass function (PMF) of the Generalized Poisson Distribution (GPD).

Usage

gpd_pmf(x, q, h, log_p = FALSE)

Arguments

x

Numeric vector of non-negative integer quantiles.

q

Parameter q > 0 (mean parameter when h = 0).

h

Parameter 0 \le h < 1 (dispersion parameter).

log_p

Logical; if TRUE, probabilities are given as \log(p). Default is FALSE.

Value

Numeric vector of PMF values.

References

Joe, H., & Zhu, R. (2005). Generalized Poisson distribution: the property of mixture of Poisson and comparison with negative binomial distribution. Biometrical Journal, 47(2), 219-229.

Examples

gpd_pmf(x = 0:10, q = 3.0, h = 0.2)

Random Generation for Generalized Poisson Distribution

Description

Generates random variates from the Generalized Poisson Distribution (GPD).

Usage

gpd_random(n, q, h)

Arguments

n

Number of observations to sample.

q

Parameter q > 0.

h

Parameter 0 \le h < 1.

Value

Numeric vector of random counts.

Examples

set.seed(123)
gpd_random(n = 20, q = 3.0, h = 0.2)

LogLik Method for GPD MLE

Description

LogLik Method for GPD MLE

Usage

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

Arguments

object

Object of class "gpd_mle".

...

Additional arguments.

Value

An object of class "logLik" containing the maximum log-likelihood value of the fitted GPD model, with attributes "df" (degrees of freedom, equal to 2) and "nobs" (number of observed failures m).

Plot Method for GPD Bayesian MCMC Diagnostics

Description

Plot Method for GPD Bayesian MCMC Diagnostics

Usage

## S3 method for class 'gpd_bayes'
plot(x, ...)

Arguments

x

Object of class "gpd_bayes".

...

Additional arguments.

Value

No return value, called for side effects. Generates MCMC diagnostic trace plots and posterior distribution histograms for parameters q and h.

Plot Profile Log-Likelihood Curves for GPD Parameters

Description

Computes and plots the profile log-likelihood curves for the parameters q and h of the Generalized Poisson Distribution (GPD) under progressive Type-II censoring (Figures 3 and 4 in Ahmad and Mansour, 2026).

Usage

plot_profile_loglik(
  x,
  R,
  param = c("both", "q", "h"),
  grid_len = 50,
  q_range = NULL,
  h_range = NULL,
  main = NULL
)

Arguments

x

Numeric vector of observed tie-free failure times (x_1 < x_2 < \dots < x_m).

R

Numeric vector of progressive removal counts (R_1, R_2, \dots, R_m).

param

Character string specifying parameter to profile: "q" or "h". If "both" (default), produces side-by-side plots for both parameters.

grid_len

Integer specifying the number of evaluation points along the profile grid. Default is 50.

q_range

Numeric vector of length 2 specifying range for q. If NULL, automatically determined around MLE.

h_range

Numeric vector of length 2 specifying range for h. If NULL, automatically determined around MLE.

main

Optional title for plot.

Value

Invisible list containing grid points and profile log-likelihood values.

References

Examples

# NF2 Spinal Tumors dataset profile log-likelihood
x_tumor <- c(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16)
R_tumor <- c(69, 12, 14, 5, 6, 4, 8, 8, 0, 1, 4, 0, 0, 0, 0, 11)
plot_profile_loglik(x = x_tumor, R = R_tumor, param = "both")

Print Method for GOF Bootstrap Test Result

Description

Print Method for GOF Bootstrap Test Result

Usage

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

Arguments

x

Object of class "gof_bootstrap".

...

Additional arguments.

Value

Invisibly returns the input object x of class "gof_bootstrap". Called for its side effect of printing the goodness-of-fit test statistic, bootstrap replicates, Monte Carlo p-value, and test decision to the console.

Print Method for GPD Bayesian MCMC Estimation

Description

Print Method for GPD Bayesian MCMC Estimation

Usage

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

Arguments

x

Object of class "gpd_bayes".

...

Additional arguments.

Value

Invisibly returns the input object x of class "gpd_bayes". Called for its side effect of printing Bayesian posterior point estimates and MCMC acceptance rates to the console.

Print Method for GPD MLE

Description

Print Method for GPD MLE

Usage

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

Arguments

x

Object of class "gpd_mle".

...

Additional arguments.

Value

Invisibly returns the input object x of class "gpd_mle". Called for its side effect of printing the GPD maximum likelihood parameter estimates and log-likelihood value to the console.

Print Method for Tie-Free Progressive Type-II Sample

Description

Print Method for Tie-Free Progressive Type-II Sample

Usage

## S3 method for class 'tiefree_p2c'
print(x, ...)

Arguments

x

An object of class "tiefree_p2c".

...

Additional arguments.

Value

Invisibly returns the input object x of class "tiefree_p2c". Called for its side effect of printing details of the tie-free progressive Type-II sample to the console.

Compute Discrete Probabilities and Event Metrics for GPD

Description

Computes specific discrete probabilities such as P(X = x), P(X > k), P(X \ge k), P(X < k), or P(X \le k).

Usage

prob_gpd(q, h, type = c("eq", "gt", "gte", "lt", "lte"), x = 0, k = 0)

Arguments

q

Parameter q > 0.

h

Parameter 0 \le h < 1.

type

Character string indicating the probability type: "eq" for P(X = x), "gt" for P(X > k), "gte" for P(X \ge k), "lt" for P(X < k), "lte" for P(X \le k).

x

Non-negative integer for type = "eq".

k

Non-negative integer bound for inequalities.

Value

Numeric probability value.

Examples

prob_gpd(q = 5.62, h = 0.75, type = "eq", x = 0)
prob_gpd(q = 5.62, h = 0.75, type = "gt", k = 10)

Spinal Tumors Count Dataset in Neurofibromatosis Type 2 (NF2) Patients

Description

Dataset containing spinal tumor counts from 158 patients with Neurofibromatosis Type 2 (NF2), originally presented by Joe and Zhu (2005) and analyzed under progressive censoring by Ahmad and Mansour (2026).

Usage

spinal_tumors

Format

A data frame with 22 rows and 2 variables:

tumor_count: Number of spinal tumors observed in a patient.
frequency: Number of patients exhibiting the given tumor count.

Source

Joe, H., & Zhu, R. (2005). Generalized Poisson distribution: the property of mixture of Poisson and comparison with negative binomial distribution. Biometrical Journal, 47(2), 219-229.

References

Ahmad, H. H., & Mansour, M. M. M. (2026). An Algorithm for Generating Tie-Free Progressive Type-II Censored Samples From Discrete Distributions. Journal of Mathematics, 2026, 3657078.

Summary Method for GPD Bayesian MCMC Estimation

Description

Summary Method for GPD Bayesian MCMC Estimation

Usage

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

Arguments

object

Object of class "gpd_bayes".

...

Additional arguments.

Value

Invisibly returns the input object object of class "gpd_bayes". Called for its side effect of displaying posterior point estimates, posterior standard errors, and credible intervals in tabular format.

Summary Method for GPD MLE

Description

Summary Method for GPD MLE

Usage

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

Arguments

object

Object of class "gpd_mle".

...

Additional arguments.

Value

Invisibly returns the input object object of class "gpd_mle". Called for its side effect of printing a detailed summary matrix containing MLE estimates, standard errors, and asymptotic confidence intervals.

Vcov Method for GPD MLE

Description

Vcov Method for GPD MLE

Usage

## S3 method for class 'gpd_mle'
vcov(object, ...)

Arguments

object

Object of class "gpd_mle".

...

Additional arguments.

Value

A 2x2 numeric variance-covariance matrix of class "matrix" with row and column names c("q", "h"), containing the estimated asymptotic covariances of the maximum likelihood estimates.

Welcome to ClientVPS Mirrors

Package {TieFreeCensor}

Coef Method for GPD MLE

Description

Usage

Arguments

Value

COVID-19 Daily Death Counts Dataset

Description

Usage

Format

Source

References

Bayesian Estimation for GPD Under Progressive Type-II Censoring

Description

Usage

Arguments

Value

References

Examples

Maximum Likelihood Estimation for GPD Under Progressive Type-II Censoring

Description

Usage

Arguments

Value

References

Examples

Generate Tie-Free Progressive Type-II Censored Samples

Description

Usage

Arguments

Value

References

Examples

Likelihood-Based Parametric Bootstrap Goodness-of-Fit Test

Description

Usage

Arguments

Value

References

Examples

Generalized Poisson Distribution Cumulative Distribution Function

Description

Usage

Arguments

Value

Examples

Generalized Poisson Distribution (GPD) Probability Mass Function

Description

Usage

Arguments

Value

References

Examples

Random Generation for Generalized Poisson Distribution

Description

Usage

Arguments

Value

Examples

LogLik Method for GPD MLE

Description

Usage

Arguments

Value

Plot Method for GPD Bayesian MCMC Diagnostics

Description

Usage

Arguments

Value

Plot Profile Log-Likelihood Curves for GPD Parameters

Description

Usage

Arguments

Value

References

Examples

Print Method for GOF Bootstrap Test Result

Description

Usage