| Title: | Point and Interval Prediction for Censored Data under Various Hybrid Censoring Schemes |
|---|---|
| Description: | Implements generalized statistical point prediction and prediction intervals for future failure times under various hybrid censoring schemes. Supported censoring schemes include Type-I, Type-II, Generalized Type-I, Generalized Type-II, Unified, Progressive Type-I, and Progressive Type-II hybrid censoring schemes. Available prediction methods include Best Unbiased Predictor (BUP), Conditional Median Predictor (CMP), Maximum Likelihood Predictor (MLP), equal-tailed classical prediction intervals, Highest Conditional Density (HCD) prediction intervals, and Bayesian prediction intervals. Algorithms accept user-defined continuous probability density functions, cumulative distribution functions, quantile functions, or survival functions along with estimated parameter values. Methodological foundations are based on Balakrishnan, Cramer, and Kundu (2023, ISBN:978-0123983879), Shafay and Balakrishnan (2012) <doi:10.1080/03610918.2011.579367> for Type-I hybrid censoring, Balakrishnan and Shafay (2012) <doi:10.1080/03610926.2010.543300> for Type-II hybrid censoring, Shafay (2017) <doi:10.1080/03610926.2016.1200093> for Generalized Type-I hybrid censoring, Shafay (2016) <doi:10.1080/00949655.2015.1096361> for Generalized Type-II hybrid censoring, Mohie El-Din, Nagy, and Shafay (2017) <doi:10.18576/jsap/060113> for Unified hybrid censoring, Ebrahimi (1992) <doi:10.1109/24.126685>, Valiollahi, Asgharzadeh, and Kundu (2017) <doi:10.1214/15-BJPS302>, and Asgharzadeh, Valiollahi, and Kundu (2015) <doi:10.1080/00949655.2013.848451>. |
| Authors: | Shikhar Tyagi [aut, cre] (ORCID: <https://orcid.org/0000-0003-1606-0844>), Arvind Pandey [aut], Bhupendra Singh [aut], Vrijesh Tripathi [aut] |
| Maintainer: | Shikhar Tyagi <[email protected]> |
| License: | GPL-3 |
| Version: | 0.1.0 |
| Built: | 2026-10-05 10:54:51 UTC |
| Source: | https://github.com/cran/predHCS |
Implements generalized statistical point prediction and prediction intervals for future failure times under various hybrid censoring schemes. Supported censoring schemes include Type-I, Type-II, Generalized Type-I, Generalized Type-II, Unified, Progressive Type-I, and Progressive Type-II hybrid censoring schemes.
| Package: | predHCS |
| Type: | Package |
| Version: | 0.1.0 |
| Date: | 2026-07-25 |
| License: | GPL-3 |
The main function is predict_censored, which acts as a unified interface for point and interval prediction under any supported hybrid censoring scheme.
Shikhar Tyagi, Arvind Pandey, Bhupendra Singh, Vrijesh Tripathi
Maintainer: Shikhar Tyagi <[email protected]>
Balakrishnan, N., Cramer, E., & Kundu, D. (2023). Hybrid censoring know-how: Designs and implementations. Academic Press.
Shafay, A. R., & Balakrishnan, N. (2012). One- and two-sample Bayesian prediction intervals based on Type-I hybrid censored data. Communications in Statistics - Theory and Methods, 41(1), 65-88.
Balakrishnan, N., & Shafay, A. R. (2012). One- and two-sample Bayesian prediction intervals based on Type-II hybrid censored data. Communications in Statistics - Theory and Methods, 41(8), 1411-1431.
Shafay, A. R. (2017). Bayesian estimation and prediction based on generalized Type-I hybrid censored sample. Communications in Statistics - Theory and Methods, 46(10), 4870-4887.
Shafay, A. R. (2016). Bayesian estimation and prediction based on generalized Type-II hybrid censored sample. Journal of Statistical Computation and Simulation, 86(10), 1970-1988.
Mohie El-Din, M. M., Nagy, M., & Shafay, A. R. (2017). Statistical inference under unified hybrid censoring scheme. Journal of Statistics Applications & Probability, 6(1), 149-167.
Ebrahimi, N. (1992). Prediction of failure times, given information on failure times of composite subsystems. Journal of Statistical Planning and Inference, 33(2), 241-256.
Valiollahi, R., Asgharzadeh, A., & Kundu, D. (2017). Prediction of future failures for generalized exponential distribution under Type-I or Type-II hybrid censoring. Brazilian Journal of Probability and Statistics, 31(1), 41-61.
Asgharzadeh, A., Valiollahi, R., & Raqab, M. Z. (2015). Stress-strength reliability of Weibull distribution under progressive Type-II censoring. Communications in Statistics - Theory and Methods, 44(8), 1618-1631.
data_obs <- c(0.5, 1.2, 2.1, 3.4, 4.0) cdf_exp <- function(x, par) pexp(x, rate = par[1]) res <- predict_censored(data = data_obs, n = 10, scheme = "Type-I", r = 6, T0 = 5.0, s = 1:2, cdf = cdf_exp, param = 0.5) print(res)data_obs <- c(0.5, 1.2, 2.1, 3.4, 4.0) cdf_exp <- function(x, par) pexp(x, rate = par[1]) res <- predict_censored(data = data_obs, n = 10, scheme = "Type-I", r = 6, T0 = 5.0, s = 1:2, cdf = cdf_exp, param = 0.5) print(res)
Print, summary, and plot methods for objects of class predhcs.
## S3 method for class 'predhcs' print(x, ...) ## S3 method for class 'predhcs' summary(object, ...) ## S3 method for class 'predhcs' plot(x, ...)## S3 method for class 'predhcs' print(x, ...) ## S3 method for class 'predhcs' summary(object, ...) ## S3 method for class 'predhcs' plot(x, ...)
x |
An object of class |
object |
An object of class |
... |
Additional arguments. |
print and summary invisibly return the object. plot creates a graphical display.
data_obs <- c(0.4, 0.8, 1.3, 2.1, 3.0) cdf_exp <- function(x, par) pexp(x, rate = par[1]) res <- pred_type1_hybrid(data = data_obs, n = 10, r = 6, T0 = 4.0, s = 1:2, cdf = cdf_exp, param = 0.5) print(res) summary(res) plot(res)data_obs <- c(0.4, 0.8, 1.3, 2.1, 3.0) cdf_exp <- function(x, par) pexp(x, rate = par[1]) res <- pred_type1_hybrid(data = data_obs, n = 10, r = 6, T0 = 4.0, s = 1:2, cdf = cdf_exp, param = 0.5) print(res) summary(res) plot(res)
Unified entry point function to perform point prediction (BUP, CMP, MLP, Bayesian) and interval prediction (Classical, HCD, Bayesian) under various hybrid censoring schemes.
predict_censored(data, n, scheme = c("Type-I", "Type-II", "Gen-Type-I", "Gen-Type-II", "Unified", "Prog-Type-I", "Prog-Type-II"), T0 = NULL, T1 = NULL, T2 = NULL, r = NULL, k = NULL, R = NULL, s = 1, cdf = NULL, pdf = NULL, qdf = NULL, surv = NULL, param = NULL, conf.level = 0.95, bayes.draws = NULL)predict_censored(data, n, scheme = c("Type-I", "Type-II", "Gen-Type-I", "Gen-Type-II", "Unified", "Prog-Type-I", "Prog-Type-II"), T0 = NULL, T1 = NULL, T2 = NULL, r = NULL, k = NULL, R = NULL, s = 1, cdf = NULL, pdf = NULL, qdf = NULL, surv = NULL, param = NULL, conf.level = 0.95, bayes.draws = NULL)
data |
Numeric vector of observed failure times. |
n |
Total initial sample size. |
scheme |
Character string specifying the hybrid censoring scheme. |
T0 |
Pre-fixed termination or inspection time threshold. |
T1 |
First time threshold for Unified scheme. |
T2 |
Second time threshold for Unified scheme. |
r |
Target number of failures. |
k |
Lower threshold for failure count. |
R |
Numeric vector of progressive removals. |
s |
Integer or vector of integers specifying future failure steps to predict. |
cdf |
Optional user-defined cumulative distribution function. |
pdf |
Optional user-defined probability density function. |
qdf |
Optional user-defined quantile function. |
surv |
Optional user-defined survival function. |
param |
Parameter vector or list for the distribution. |
conf.level |
Confidence level for prediction intervals (default 0.95). |
bayes.draws |
Optional matrix of MCMC posterior draws for Bayesian prediction. |
An object of class predhcs containing prediction results.
data_obs <- c(0.4, 0.8, 1.3, 2.1, 3.0) cdf_exp <- function(x, par) pexp(x, rate = par[1]) res1 <- predict_censored(data = data_obs, n = 10, scheme = "Type-I", r = 6, T0 = 4.0, s = 1:2, cdf = cdf_exp, param = 0.5) print(res1)data_obs <- c(0.4, 0.8, 1.3, 2.1, 3.0) cdf_exp <- function(x, par) pexp(x, rate = par[1]) res1 <- predict_censored(data = data_obs, n = 10, scheme = "Type-I", r = 6, T0 = 4.0, s = 1:2, cdf = cdf_exp, param = 0.5) print(res1)
Functions to compute point predictions and prediction intervals under specific hybrid censoring schemes.
pred_type1_hybrid(data, n, r, T0, s = 1, cdf = NULL, pdf = NULL, qdf = NULL, surv = NULL, param = NULL, conf.level = 0.95, bayes.draws = NULL) pred_type2_hybrid(data, n, r, T0, s = 1, cdf = NULL, pdf = NULL, qdf = NULL, surv = NULL, param = NULL, conf.level = 0.95, bayes.draws = NULL) pred_gen_type1_hybrid(data, n, k, r, T0, s = 1, cdf = NULL, pdf = NULL, qdf = NULL, surv = NULL, param = NULL, conf.level = 0.95, bayes.draws = NULL) pred_gen_type2_hybrid(data, n, k, r, T0, s = 1, cdf = NULL, pdf = NULL, qdf = NULL, surv = NULL, param = NULL, conf.level = 0.95, bayes.draws = NULL) pred_unified_hybrid(data, n, k, r, T1, T2, s = 1, cdf = NULL, pdf = NULL, qdf = NULL, surv = NULL, param = NULL, conf.level = 0.95, bayes.draws = NULL) pred_prog_type1_hybrid(data, n, R, T0, s = 1, cdf = NULL, pdf = NULL, qdf = NULL, surv = NULL, param = NULL, conf.level = 0.95, bayes.draws = NULL) pred_prog_type2_hybrid(data, n, R, T0, s = 1, cdf = NULL, pdf = NULL, qdf = NULL, surv = NULL, param = NULL, conf.level = 0.95, bayes.draws = NULL)pred_type1_hybrid(data, n, r, T0, s = 1, cdf = NULL, pdf = NULL, qdf = NULL, surv = NULL, param = NULL, conf.level = 0.95, bayes.draws = NULL) pred_type2_hybrid(data, n, r, T0, s = 1, cdf = NULL, pdf = NULL, qdf = NULL, surv = NULL, param = NULL, conf.level = 0.95, bayes.draws = NULL) pred_gen_type1_hybrid(data, n, k, r, T0, s = 1, cdf = NULL, pdf = NULL, qdf = NULL, surv = NULL, param = NULL, conf.level = 0.95, bayes.draws = NULL) pred_gen_type2_hybrid(data, n, k, r, T0, s = 1, cdf = NULL, pdf = NULL, qdf = NULL, surv = NULL, param = NULL, conf.level = 0.95, bayes.draws = NULL) pred_unified_hybrid(data, n, k, r, T1, T2, s = 1, cdf = NULL, pdf = NULL, qdf = NULL, surv = NULL, param = NULL, conf.level = 0.95, bayes.draws = NULL) pred_prog_type1_hybrid(data, n, R, T0, s = 1, cdf = NULL, pdf = NULL, qdf = NULL, surv = NULL, param = NULL, conf.level = 0.95, bayes.draws = NULL) pred_prog_type2_hybrid(data, n, R, T0, s = 1, cdf = NULL, pdf = NULL, qdf = NULL, surv = NULL, param = NULL, conf.level = 0.95, bayes.draws = NULL)
data |
Numeric vector of observed failure times. |
n |
Total initial sample size. |
r |
Target number of failures. |
k |
Lower threshold for failure count. |
T0 |
Termination time threshold. |
T1 |
First time threshold for Unified scheme. |
T2 |
Second time threshold for Unified scheme. |
R |
Progressive removals vector. |
s |
Future failure step(s) to predict. |
cdf |
Optional user CDF. |
pdf |
Optional user PDF. |
qdf |
Optional user Quantile function. |
surv |
Optional user Survival function. |
param |
Distribution parameters. |
conf.level |
Confidence level for prediction intervals. |
bayes.draws |
Optional MCMC posterior draws matrix. |
An object of class predhcs containing prediction results.
data_obs <- c(0.5, 1.2, 2.1, 3.4, 4.0) cdf_exp <- function(x, par) pexp(x, rate = par[1]) res <- pred_type1_hybrid(data = data_obs, n = 10, r = 6, T0 = 5.0, s = 1:2, cdf = cdf_exp, param = 0.5) print(res)data_obs <- c(0.5, 1.2, 2.1, 3.4, 4.0) cdf_exp <- function(x, par) pexp(x, rate = par[1]) res <- pred_type1_hybrid(data = data_obs, n = 10, r = 6, T0 = 5.0, s = 1:2, cdf = cdf_exp, param = 0.5) print(res)