Search Results (14)

To reduce reliability testing time, experiments are often terminated at a predetermined time, producing right-censored lifetime data. Alternatively, when test samples are inspected at fixed intervals, failures are only observed within these intervals, resulting in interval-censored lifetime data. Although quality control methods for right-censored data are well established, relatively little attention has been given to interval-censored observations. Motivated by the success of residual control charts based on convolutional neural network (CNN) for right-censored data, this study extends the chart for monitoring normally distributed interval-censored lifetime data. Simulation results based on average run length (ARL) indicate that the proposed method outperforms the traditional exponentially weighted moving average (EWMA) chart in detecting decreases in mean lifetime. The findings also highlight the practical benefits of employing high- or low-order autoregressive CNN models depending on the magnitude of process shifts. Full article

We develop a unified likelihood-based framework for limited outcomes built on the two-piece normal family. The framework includes a censored specification that accommodates boundary inflation, a doubly truncated specification on $(0,1)$ for rates and proportions, and a survival formulation with a log-two-piece normal baseline and Gamma frailty to account for unobserved heterogeneity. We derive closed-form building blocks (pdf, cdf, survival, hazard, and cumulative hazard), full log-likelihoods with score functions and observed information, and stable reparameterizations that enable routine optimization. Monte Carlo experiments show a small bias and declining RMSE with increasing sample size; censoring primarily inflates the variability of regression coefficients; the scale parameter remains comparatively stable, and the shape parameter is most sensitive under heavy censoring. Applications to HIV-1 RNA with a detection limit, household food expenditure on $(0,1)$, labor-supply hours with a corner solution, and childhood cancer times to hospitalization demonstrate improved fit over Gaussian, skew-normal, and beta benchmarks according to AIC/BIC/CAIC and goodness-of-fit diagnostics, with model-implied censoring closely matching the observed fraction. The proposed formulations are tractable, flexible, and readily implementable with standard software. Full article

The increasing prominence of the problem of censored data in various fields has made studying how to perform parameter estimation and variable selection in censored mixed-effects models one of the hotspots of current research. In this paper, considering the situation that the response variable is restricted by the bilateral limit, a double-penalty Bayesian Tobit quantile regression model was constructed to carry out parameter estimation and variable selection in the interval-censored mixed-effects model, and at the same time, the fixed-effects and random effects coefficients are compressed in Tobit’s mixed-effects model, so as to reduce the estimation error of the model at the same time as the variable selection of the model is carried out. The posterior distribution of each unknown parameter was derived using the conditional Laplace prior and the mixed truncated normal distribution of interval-censored data, and then the Gibbs sampling algorithm for unknown parameter estimation was constructed. Through Monte Carlo simulation, it was found that the new method is more advantageous than the classical method in terms of variable selection and parameter estimation accuracy in various situations, such as different model sparsity, different data censoring ratios and different random error distributions, and the model is able to realize automatic variable selection. Finally, the new method is used to analyze the correlation between the crime rate and various economic indicators in China. Full article

In this study, we introduce a novel estimation technique for assessing the reliability parameter $R=P(Y<X)$ of the uniform truncated negative binomial distribution (UTNBD) in the context of stress–strength analysis. We base our inferences on the assumption that both the strength (X) and stress (Y) random variables follow a UTNBD with identical first shape and scale parameters. In the presence of a progressive type-II censoring scheme, we employ maximum likelihood, two parametric bootstrap methods, and Bayesian estimation approaches to derive the estimators. Due to the complexity introduced by censoring, the estimators are not available in explicit forms and are instead obtained through numerical approximation techniques. Furthermore, we compute the highest posterior density credible intervals and determine the asymptotic variance-covariance matrix. To assess the performance of our proposed estimators, we conduct a Monte Carlo simulation study and provide a comparative analysis. Finally, we illustrate the practical applicability of our study with an engineering application. Full article

In this article, a new modified asymmetric Topp–Leone distribution is created and developed from a theoretical and inferential point of view. It has the feature of extending the remarkable flexibility of a special one-shape-parameter lifetime distribution, known as the inverse Topp–Leone distribution, to the bounded interval $[0, 1]$. The probability density function of the proposed truncated distribution has the potential to be unimodal and right-skewed, with different levels of asymmetry. On the other hand, its hazard rate function can be increasingly shaped. Some important statistical properties are examined, including several different measures. In practice, the estimation of the model parameters under progressive type-II censoring is considered. To achieve this aim, the maximum likelihood, maximum product of spacings, and Bayesian approaches are used. The Markov chain Monte Carlo approach is employed to produce the Bayesian estimates under the squared error and linear exponential loss functions. Some simulation studies to evaluate these approaches are discussed. Two applications based on real-world datasets—one on the times of infection, and the second dataset is on trading economics credit rating—are considered. Thanks to its flexible asymmetric features, the new model is preferable to some known comparable models. Full article

In this paper, a competing risks model with dependent causes of failure is considered under left-truncated and right-censoring scenario. When the dependent failure causes follow a Marshall–Olkin bivariate exponential distribution, estimation of model parameters and reliability indices are proposed from classic and Bayesian approaches, respectively. Maximum likelihood estimators and approximate confidence intervals are constructed, and conventional Bayesian point and interval estimations are discussed as well. In addition, E-Bayesian estimators are proposed and their asymptotic behaviors have been investigated. Further, another objective-Bayesian analysis is also proposed when a noninformative probability matching prior is used. Finally, extensive simulation studies are carried out to investigate the performance of different methods. Two real data examples are presented to illustrate the applicability. Full article

Left-truncated and right-censored data are widely used in lifetime experiments, biomedicine, labor economics, and actuarial science. This article discusses how to resolve the problems of statistical inferences on the unknown parameters of the exponentiated half-logistic distribution based on left-truncated and right-censored data. In the beginning, maximum likelihood estimations are calculated. Then, asymptotic confidence intervals are constructed by using the observed Fisher information matrix. To cope with the small sample size scenario, we employ the percentile bootstrap method and the bootstrap-t method for the establishment of confidence intervals. In addition, Bayesian estimations under both symmetric and asymmetric loss functions are addressed. Point estimates are computed by Tierney–Kadane’s approximation and importance sampling procedure, which is also applied to establishing corresponding highest posterior density credible intervals. Lastly, simulated and real data sets are presented and analyzed to show the effectiveness of the proposed methods. Full article

Urinary concentrations of several endocrine disrupting chemicals, including phthalate metabolites, bisphenol A (BPA), and benzophenone (BP)-type ultraviolet (UV) filters, have been associated with a longer time-to-pregnancy (TTP). Potential modification of these associations by couple’s age has not been studied. TTP was defined as the number of prospectively observed menstrual cycles a couple attempted pregnancy until the occurrence of a human chorionic gonadotropic-detected pregnancy. Urinary concentrations of two BP-type UV filters and three phthalate metabolites were measured at baseline. Fecundability odds ratios (FORs) and 95% confidence intervals (CIs) were estimated for each chemical adjusting for age, body mass index, serum cotinine, creatinine, and accounting for right censoring and left truncation. Models evaluated effect modification between EDC concentrations and TTP by partner’s age, dichotomized at 35 years. Separate models were run for male and female partners. No significant effect modification was observed for any EDC for either partner, but data were suggestive of a longer TTP among females aged ≥35 years, particularly for BP-2 (FOR = 0.61, 95% CI 0.36, 1.05) and 4-hydroxybenzophenone (FOR = 0.71, 95% CI: 0.46, 1.09) reflecting 39% and 29% reductions in fecundability, respectively. We saw no evidence of effect modification by couples’ age on associations between TTP and urinary phthalate or BPA metabolite concentrations. Across the EDCs we examined, we found little evidence that age modifies TTP-exposure associations. Full article

There is evidence that ICT developments can improve bank efficiency and performance. Previous studies often employ data envelopment analysis (DEA) to first examine bank performance and then use a second-stage regression to explain the influences of other environmental factors, including ICT, on such efficiency. Since DEA efficiency scores are bounded between the (0, 1] intervals, Tobit and truncated regressions are commonly used in this stage. However, none has accounted for the skewness characteristic of DEA efficiency. This paper applied a bootstrap-censored quantile regression (BCQR) approach to triply account for the issues of a small sample (via bootstrap), bounded intervals (via censored regression), and skewness (via quantile regression) in DEA analysis. We empirically examined the efficiency and performance of 27 Vietnamese commercial banks in the 2007–2019 period. The efficiency scores derived from our first stage revealed that they are skewed and thus, justify the use of the BCQR in the second stage. The BCQR results further confirmed that ICT developments could enhance bank efficiency, which supports the recent policy to restructure the Vietnamese banking sector toward innovation and digitalization. We also examined the impacts of other factors such as bank ownership, credit risk, and bank size on efficiency. Full article

In this paper, statistical inference and prediction issue of left truncated and right censored dependent competing risk data are studied. When the latent lifetime is distributed by Marshall–Olkin bivariate Rayleigh distribution, the maximum likelihood estimates of unknown parameters are established, and corresponding approximate confidence intervals are also constructed by using a Fisher information matrix and asymptotic approximate theory. Furthermore, Bayesian estimates and associated high posterior density credible intervals of unknown parameters are provided based on general flexible priors. In addition, when there is an order restriction between unknown parameters, the point and interval estimates based on classical and Bayesian frameworks are discussed too. Besides, the prediction issue of a censored sample is addressed based on both likelihood and Bayesian methods. Finally, extensive simulation studies are conducted to investigate the performance of the proposed methods, and two real-life examples are presented for illustration purposes. Full article

Point and interval estimations are taken into account for a progressive first-failure censored left-truncated normal distribution in this paper. First, we derive the estimators for parameters on account of the maximum likelihood principle. Subsequently, we construct the asymptotic confidence intervals based on these estimates and the log-transformed estimates using the asymptotic normality of maximum likelihood estimators. Meanwhile, bootstrap methods are also proposed for the construction of confidence intervals. As for Bayesian estimation, we implement the Lindley approximation method to determine the Bayesian estimates under not only symmetric loss function but also asymmetric loss functions. The importance sampling procedure is applied at the same time, and the highest posterior density (HPD) credible intervals are established in this procedure. The efficiencies of classical statistical and Bayesian inference methods are evaluated through numerous simulations. We conclude that the Bayes estimates given by Lindley approximation under Linex loss function are highly recommended and HPD interval possesses the narrowest interval length among the proposed intervals. Ultimately, we introduce an authentic dataset describing the tensile strength of 50mm carbon fibers as an illustrative sample. Full article

In this paper, the parameter estimation problem of a truncated normal distribution is discussed based on the generalized progressive hybrid censored data. The desired maximum likelihood estimates of unknown quantities are firstly derived through the Newton–Raphson algorithm and the expectation maximization algorithm. Based on the asymptotic normality of the maximum likelihood estimators, we develop the asymptotic confidence intervals. The percentile bootstrap method is also employed in the case of the small sample size. Further, the Bayes estimates are evaluated under various loss functions like squared error, general entropy, and linex loss functions. Tierney and Kadane approximation, as well as the importance sampling approach, is applied to obtain the Bayesian estimates under proper prior distributions. The associated Bayesian credible intervals are constructed in the meantime. Extensive numerical simulations are implemented to compare the performance of different estimation methods. Finally, an authentic example is analyzed to illustrate the inference approaches. Full article

In reality, estimations for the unknown parameters of truncated distribution with censored data have wide utilization. Truncated normal distribution is more suitable to fit lifetime data compared with normal distribution. This article makes statistical inferences on estimating parameters under truncated normal distribution using adaptive progressive type II censored data. First, the estimates are calculated through exploiting maximum likelihood method. The observed and expected Fisher information matrices are derived to establish the asymptotic confidence intervals. Second, Bayesian estimations under three loss functions are also studied. The point estimates are calculated by Lindley approximation. Importance sampling technique is applied to discuss the Bayes estimates and build the associated highest posterior density credible intervals. Bootstrap confidence intervals are constructed for the purpose of comparison. Monte Carlo simulations and data analysis are employed to present the performances of various methods. Finally, we obtain optimal censoring schemes under different criteria. Full article

There are different patterns in the COVID-19 outbreak in the general population and amongst nursing home patients. We investigate the time from symptom onset to diagnosis and hospitalization or the length of stay (LoS) in the hospital, and whether there are differences in the population. Sciensano collected information on 14,618 hospitalized patients with COVID-19 admissions from 114 Belgian hospitals between 14 March and 12 June 2020. The distributions of different event times for different patient groups are estimated accounting for interval censoring and right truncation of the time intervals. The time between symptom onset and hospitalization or diagnosis are similar, with median length between symptom onset and hospitalization ranging between 3 and 10.4 days, depending on the age of the patient (longest delay in age group 20–60 years) and whether or not the patient lives in a nursing home (additional 2 days for patients from nursing home). The median LoS in hospital varies between 3 and 10.4 days, with the LoS increasing with age. The hospital LoS for patients that recover is shorter for patients living in a nursing home, but the time to death is longer for these patients. Over the course of the first wave, the LoS has decreased. Full article