Progressive Censored Data Research Articles

Likelihood and pivotal-based reliability inference for inverse exponentiated Rayleigh distribution under block progressive censoring

ABSTRACT In this paper, focus is on the estimation of survival characteristics, specifically the reliability function, hazard rate function, median time to failure, and differences in different test facilities, using block progressive censored data. Estimations are carried out through both maximum likelihood and pivotal methods, assuming the lifetime distribution of test units follows an inverse exponentiated Rayleigh distribution. The paper derives maximum likelihood estimators for unknown parameters, exploring their existence and uniqueness properties. Approximate confidence intervals for survival characteristics are constructed using the delta method and likelihood theory. Moreover, point and generalized confidence interval estimators are developed through a pivotal quantity-based method. A simulation study is conducted to compare the performance of the proposed approaches, revealing that the pivotal quantity-based approach yields superior estimation results. Finally, the proposed estimates are applied to analyze two real datasets, illustrating their practical applicability.

Parameter estimation of Chen distribution under improved adaptive type-II progressive censoring

ABSTRACT This study focuses on the estimation of the two unknown parameters of Chen distribution, characterized by a bathtub-shaped hazard rate function, within an improved adaptive type-II progressive censored data framework. Maximum likelihood estimation is proposed for the two parameters, and the establishment of approximate confidence intervals is based on asymptotic normality. Bayesian estimation is also conducted under both symmetric and asymmetric loss functions, utilizing the proposed importance sampling and Metropolis–Hastings algorithm. Lastly, the performance of various estimation methods is evaluated through Monte Carlo simulation experiments, and the proposed estimation approach is illustrated using a real dataset.

Analysis of a new extension version of the exponential model using improved adaptive progressive censored data and its applications

This article covers the issue of evaluating the two shape parameters and reliability metrics of a novel Kumaraswamy-exponential lifetime distribution, whose density exhibits a left-skewed, right-skewed, or symmetric shape, through a type-II improved adaptive progressively censored sample. Both conventional and Bayesian viewpoints are used to evaluate the various parameters, which include point and interval estimations. While the estimation of one of the shape parameters requires a numerical solution, the other shape parameter estimation can be carried out in closed form by the classical method. Besides, the likelihood method’s asymptotic traits are employed to provide interval estimations for all parameters. Leveraging the Markov chain Monte Carlo process, the symmetric squared loss function and independent gamma priors are taken into account for calculating Bayes points and the highest posterior density interval estimations. To illustrate the accuracy, compare estimation methods, and show the applicability of the various suggested methods, a simulation examination and a pair of applications are looked at. In the end, four accuracy indicators are taken into consideration to figure out the best progressive censoring pattern. The numerical results indicate that when collecting samples using the suggested censored procedure, it is advisable to use the Bayesian estimation approach for evaluating the Kumaraswamy-exponential distribution.

Estimation and prediction on power Muth distribution with progressive censored data: a Bayesian approach

In this paper, estimation and prediction inference of power Muth distribution, with the progressive censoring data, are described. The maximum likelihood and Bayesian approaches of the unknown parameters are considered. Several Bayesian estimators are obtained against different symmetric and asymmetric loss functions, such as squared error, linex and general entropy. Also, the asymptotic confidence intervals and highest posterior density credible intervals of them are derived. Most focus of this paper is Bayesian prediction of the removed units in multiple stages of the progressively censored sample, so that, the Gibbs and Metropolis samplers are used, to reach this end. To compare the performance of different methods, Mont Carlo simulation is employed. Moreover, one practical data set is analyzed for illustrative purposes.

Evaluation of the lifetime performance index on first failure progressive censored data based on Topp Leone Alpha power exponential model applied on HPLC data

ABSTRACT In this paper, the statistical inference of the lifetime performance index for the first failure progressive censoring schemes for the Topp Leone Alpha power exponential distribution (TLAPE) which excluded from a new structure of distribution models called T-Alpha Power X (T-APX) family is introduced. The proposed statistical inference of the lifetime performance index is applied on the High-Performance Liquid Chromatography data of blood samples from organ transplant recipients which is known as HPLC. The goodness of fit criteria of TLAPE for HPLC data proved the potentiality of TLAPE compared with other well-known distributions. This result has an effect on achieving the required results in testing procedure of the Lifetime performance index. Moreover, the statistical and reliability characteristics of TLAPE are studied. A simulation study is performed to examine the performance of the ML parameter estimates in terms of bias and mean square error. Two real data sets for survival and breast cancer are modeled using the TLAPE distribution and compared with other well-known distributions, to illustrate its performance. The results emphasize that the TLAPE distribution has a superior fitting performance to cancer data than the compared distributions.

Pivotal Inference for the Inverted Exponentiated Rayleigh Distribution Based on Progressive Type-II Censored Data

In this article, the pivotal inference is proposed to estimate the two unknown parameters of the inverse exponentiated Rayleigh distribution based on progressive censored data. We derive the point estimator and construct an interval estimator using the pivotal quantity method. To compare the performance of this proposed method and the traditional maximum likelihood estimation method, a simulation study is conducted. The simulation results show that the proposed method performs better in terms of bias and mean squared error. Finally, a real dataset is used to illustrate the proposed approaches.

A Mortality Approach for Estimating the Probability of Default in Credit Risk

Credit risk is an important problem in banking, finance and insurance sectors. The financial institutions have to use information related to some specific characteristics of borrowers, such as borrower reputation, capital and capacity in order to make the right decision whether or not to grant credit. Regulatory capital allows banks to better capture unique risks and exposure cash flows. In this work, we propose a new approach to estimate the probability of default (PD) by using mortality tables based on progressive censored. The PD is a crucial value, which is used in computing the required capital against credit risk exposures. We use the internal rate approach and measure the PD based on time of default. Then we create a new model for Progressive censored data. The new model takes advantage simultaneously from both the progressively censored and Moody’s models, and where the objective is to compute the cumulative probability. The overall proposed approach is illustrated by examples to show its applicability and demonstrate its performance. Our research findings show that the PD based survival analysis for progressive censored increases each year similar to Moody’s. It impacts on worst –case default rate and the maturity adjustment.

A new test statistic to assess the goodness of fit of exponential distribution under progressive censoring

The problem of examining how well a assumed distribution fits the data of a sample is of significant that has to be examined prior to any inferential process. In this paper, a new goodness-of-fit test for an exponential distribution based on progressive censored data is proposed. Using Monte Carlo simulation studies, the present researchers have observed that the proposed test for exponentiality is consistent and quite powerful in comparison with existing goodness-of-fit tests based on progressive censored data. Also, the new test statistic for a real data set is used and the results show that our new test statistic performs well.

Bayesian and classical estimation of reliability in a multicomponent stress-strength model under adaptive hybrid progressive censored data

The statistical inference of multicomponent stress-strength reliability under the adaptive Type-II hybrid progressive censored samples for the Weibull distribution is considered. It is assumed that both stress and strength are two Weibull independent random variables. We study the problem in three cases. First assuming that the stress and strength have the same shape parameter and different scale parameters, the maximum likelihood estimation (MLE), approximate maximum likelihood estimation (AMLE) and two Bayes approximations, due to the lack of explicit forms, are derived. Also, the asymptotic confidence intervals, two bootstrap confidence intervals and highest posterior density (HPD) credible intervals are obtained. In the second case, when the shape parameter is known, MLE, exact Bayes estimation, uniformly minimum variance unbiased estimator (UMVUE) and different confidence intervals (asymptotic and HPD) are studied. Finally, assuming that the stress and strength have the different shape and scale parameters, ML, AML and Bayesian estimations on multicomponent reliability have been considered. The performances of different methods are compared using the Monte Carlo simulations and for illustrative aims, one data set is investigated.

Statistical inferences for new Weibull-Pareto distribution under an adaptive type-ii progressive censored data

In this paper, we obtain the maximum likelihood, Bayes and parametric bootstrap estimators for the parameters of a new Weibull-Pareto distribution (NWPD) and some lifetime indices such as reliability function S(t), failure rate h(t) function and coefficient of variation CV are obtained. The previous methods are studied in the case of an adaptive Type-II progressive censoring (Ada-T-II-Pro-C). Approximate confidence intervals (ACIs) of the unknown parameters are constructed based on the asymptotic normality of maximum likelihood estimators (MLEs). Bayes estimates and the symmetric credible intervals (CRIs) of the unknown quantities are calculated based on the Gibbs sampler within Metropolis– Hasting (M-H) algorithm procedure. The results of Bayes estimates are obtained under the consideration of the informative prior function with respect to the squared error loss (SEL) function. Two numerical examples are presented to illustrate the proposed methods, one of them is a simulated example and the other is a real life example. Finally, the performance of different Bayes estimates are compared with maximum likelihood (ML) and two parametric bootstrap estimates, through a Monte Carlo simulation study.

On generalized progressive hybrid censoring in presence of competing risks

The progressive Type-II hybrid censoring scheme introduced by Kundu and Joarder (Comput Stat Data Anal 50:2509–2528, 2006), has received some attention in the last few years. One major drawback of this censoring scheme is that very few observations (even no observation at all) may be observed at the end of the experiment. To overcome this problem, Cho et al. (Stat Methodol 23:18–34, 2015) recently introduced generalized progressive censoring which ensures to get a pre specified number of failures. In this paper we analyze generalized progressive censored data in presence of competing risks. For brevity we have considered only two competing causes of failures, and it is assumed that the lifetime of the competing causes follow one parameter exponential distributions with different scale parameters. We obtain the maximum likelihood estimators of the unknown parameters and also provide their exact distributions. Based on the exact distributions of the maximum likelihood estimators exact confidence intervals can be obtained. Asymptotic and bootstrap confidence intervals are also provided for comparison purposes. We further consider the Bayesian analysis of the unknown parameters under a very flexible beta–gamma prior. We provide the Bayes estimates and the associated credible intervals of the unknown parameters based on the above priors. We present extensive simulation results to see the effectiveness of the proposed method and finally one real data set is analyzed for illustrative purpose.

Bayesian Inference for Step-Stress Partially Accelerated Competing Failure Model under Type II Progressive Censoring

This paper deals with the Bayesian inference on step-stress partially accelerated life tests using Type II progressive censored data in the presence of competing failure causes. Suppose that the occurrence time of the failure cause follows Pareto distribution under use stress levels. Based on the tampered failure rate model, the objective Bayesian estimates, Bayesian estimates, and E-Bayesian estimates of the unknown parameters and acceleration factor are obtained under the squared loss function. To evaluate the performance of the obtained estimates, the average relative errors (AREs) and mean squared errors (MSEs) are calculated. In addition, the comparisons of the three estimates of unknown parameters and acceleration factor for different sample sizes and different progressive censoring schemes are conducted through Monte Carlo simulations.

On Parameters Estimation of Lomax Distribution under General Progressive Censoring

We consider the estimation problem of the probability S=P(Y<X) for Lomax distribution based on general progressive censored data. The maximum likelihood estimator and Bayes estimators are obtained using the symmetric and asymmetric balanced loss functions. The Markov chain Monte Carlo (MCMC) methods are used to accomplish some complex calculations. Comparisons are made between Bayesian and maximum likelihood estimators via Monte Carlo simulation study.

Predicting observables from Weibull model based on general progressive censored data with asymmetric loss

The objective of this paper is to develop a methodology to construct and compute in a Bayesian setting, point and interval predictions based on general progressive Type-II censored data from Weibull model. Prediction bounds for the future observations (2-sample prediction) based on this type of censored will be derived. Bayesian predictions are obtained based on a continuous–discrete joint prior for the unknown two parameters. We have examined point predictions under symmetric and asymmetric loss functions. As application, the total duration time in a life test and the failure time of a k -out-of- m system may be predicted. An illustrative example consisting of various types of real data from an accelerated test on insulating fluid reported by Nelson (1982) [17] is presented. Finally, some numerical results using simulation study concerning different sample sizes, and different progressive censoring schemes were reported. A study of 10 000 randomly generated future samples from the same distribution shows that the actual prediction levels are satisfactory.

Fisher information and optimal schemes in progressive Type-II censored samples

This article deals with two results for the computation of the Fisher information (FI) in progressive Type-II censored data; the results simplifies the calculation of the FI in any progressive censored data. The FI is presented as a sum of the FI in the smallest order statistics. The results are used to obtain the optimal censoring schemes in the progressive Type-II censored data for two optimality criteria that are based on the inverse of the exact FI. The methodology is illustrated with the normal and the Weibull distributions, which are popular models in the lifetime analysis.

Prediction of Progressive Censored Data from the Gompertz Model

Progressive type-II censored sampling is an important scheme of obtaining data in lifetime studies. This article is concerned with the problem of obtaining Bayesian prediction bounds for future order statistics from the two-parameter Gompertz distribution based on progressive type-II censored data using the two-sample prediction technique. An algorithm due to Balakrishnan and Sandhu (Balakrishnan, N., Sandhu, R. A. (1995). A simple algorithm for generating progressive type-II censored samples. American Statistician 49(2):229–230.) and Aggarwala and Balakrishnan (Aggarwala, R., Balakrishnan, N. (1998a). Some properties of progressive censored order statistics from arbitary and uniform distributions with applications to inference and simulation. J. Statist. Plain. Inference 70:35–49.) was used to generate progressive type-II censored samples from the Gompertz distribution and the accuracy of prediction intervals is investigated via Monte Carlo simulation.