Search Results (18)

Kernel density estimation for right-censored data has been extensively studied in the non-recursive setting, whereas recursive approaches adapted to censoring remain largely unexplored despite their considerable computational advantages in sequential data environments. In this paper, we introduce a recursive kernel density estimator for independent right-censored observations through a Kaplan-Meier weighting scheme. The proposed estimator can be updated incrementally as new observations become available, avoiding repeated re-computation of the entire estimator and substantially reducing memory and computational requirements. Under mild regularity conditions, we establish the asymptotic normality of the estimator and derive its asymptotic variance, which explicitly reflects the effect of the recursive weighting mechanism and the censoring process. We also construct asymptotic confidence intervals for the underlying density using a plug-in variance estimator. An extensive Monte Carlo study, including Gaussian, exponential, heavy-tailed, multimodal, contaminated, and severely censored scenarios, demonstrates that the proposed estimator achieves estimation accuracy comparable to that of the classical censored Parzen-Rosenblatt estimator while offering substantial computational gains. In particular, the recursive procedure remains stable under high censoring levels and exhibits excellent scalability for large and sequentially collected datasets. The proposed methodology provides an efficient and theoretically justified alternative for nonparametric density estimation under right censoring and is particularly suited to applications involving streaming data, such as survival analysis, reliability engineering, medical monitoring, and online forecasting. Full article

In this paper, we introduce a new age-dependent reliability class, termed the new better (worse) than renewal used in Laplace transform order after age $t_0$ ($NBRU{L}^{\ast }{t}_0$). This class extends existing aging notions by characterizing lifetime distributions through renewal-based Laplace transform ordering beyond a specified age threshold. Several theoretical properties of the proposed class are established, including its relationships with classical aging classes. A goodness-of-fit test for exponentiality against the $NBRU{L}^{\ast }{t}_0$ alternative is developed using the framework of U-statistics, yielding a scale-invariant test statistic with a tractable asymptotic distribution. The asymptotic normality and Pitman asymptotic efficiency of the proposed test are derived, demonstrating superior efficiency relative to several existing nonparametric competitors. Extensive Monte Carlo simulations are conducted to obtain critical values and to assess the power performance of the test under both complete and randomly right-censored samples. The results indicate that the proposed test exhibits high power and robustness, particularly in the presence of aging effects and censoring. Applications to real engineering and medical datasets illustrate the practical relevance of the $NBRU{L}^{\ast }{t}_0$ class in reliability analysis and survival studies. Full article

This study explores classical and Bayesian estimation for the two-parameter Chen distribution with randomly censored data, where censoring times follow an independent two-parameter Chen distribution with separate shape and scale parameters. We first derive the maximum likelihood estimators of the unknown parameters, together with their asymptotic variances and credible intervals, and further adopt the method of moments, L-moments and least squares methods for classical estimation. Under the generalized entropy loss function and inverse gamma priors, Bayesian estimation is implemented via Gibbs sampling, with the highest posterior density credible intervals of parameters constructed accordingly. We also investigate the estimation of key reliability and lifetime characteristics of the distribution, and conduct Monte Carlo simulations to compare the performance of all aforementioned estimation methods. Finally, two real-world CMAPSS jet engine lifetime datasets from NASA are applied to validate the practical effectiveness of the proposed estimation approaches, demonstrating the enhanced flexibility of the Chen distribution compared to the exponential distribution in fitting aerospace-related censored data, given the marginal p-values in the K-S tests. Full article

This paper investigates the problem of parameter estimation and reliability analysis for the two-parameter Maxwell distribution under a random censoring mechanism. To address the limitation of the traditional single-parameter Maxwell distribution in practical applications, which lacks the threshold parameter, this paper proposes a two-parameter Maxwell distribution model. By introducing a threshold parameter, this model can more accurately characterize survival data with a minimum life or guaranteed operating time. Specifically, we construct a random censoring data model wherein both the failure time and censoring time are assumed to follow a two-parameter Maxwell distribution. The main research contents include: establishing a randomly censored data model, deriving classical inference methods based on maximum likelihood estimation. Under the general entropy loss function, Bayesian estimation is conducted using conjugate inverse Gamma priors for scale parameters and a uniform prior for the threshold parameter. A hybrid MCMC algorithm is implemented to generate posterior samples and construct highest posterior density credible intervals. We compare their performance through Monte Carlo simulations, evaluating finite-sample behavior in terms of bias, mean squared error, and interval estimation, and finally validating the practicality and superiority of the two-parameter model using real medical datasets from a colon cancer clinical trial. The results demonstrate that the two-parameter Maxwell distribution can more accurately describe survival data with threshold characteristics and outperforms the single-parameter model in terms of model fit and reliability estimation. Full article

This study focuses on parameter estimation and reliability analysis for the two-parameter Rayleigh distribution under random censoring. It is shown that directly fitting the standard Rayleigh distribution can lead to substantial estimation errors, especially when the dataset contains a markedly high minimum value. To overcome the limitation of the conventional single-parameter Rayleigh distribution, which lacks a threshold parameter in practical applications, a two-parameter Rayleigh distribution model is proposed. The main research contents include the following: establishing a randomly censored data model; deriving classical inference methods based on maximum likelihood estimation along with several other classical estimation techniques; and constructing a Bayesian estimation framework. We also analyze several reliability and experimental characteristics by deriving their corresponding estimates. A Monte Carlo simulation study is carried out to assess the performance of the proposed estimators. Finally, the practicality and superiority of the two-parameter model are validated using real strength datasets. The results demonstrate that the two-parameter Rayleigh distribution can more accurately describe survival data with threshold characteristics and outperforms the single-parameter model in terms of model fit and reliability estimation. Full article

Counting data play a critical role in various real-life applications across different scientific fields. This study handles the classical and Bayesian estimation of the one-parameter discrete linear exponential distribution under randomly right-censored data. Maximum likelihood estimators, both point and interval, are derived for the unknown parameter. In addition, Bayesian estimators are gained using informative and non-informative priors, assessed under three distinct loss functions: squared error loss, linear exponential loss, and generalized entropy loss. An algorithm for generating randomly right-censored data from the proposed model is also developed. To evaluate the efficiency of the estimators, considerable simulation studies are conducted, revealing that the maximum likelihood and the Bayesian approach under the generalized entropy loss function with a positive weight consistently outperform other methods across all sample sizes, achieving the lowest root mean squared errors. Finally, the discrete linear exponential distribution demonstrates strong applicability in modeling discrete count lifetime data in physical and medical sciences, outperforming related alternative distributions. Full article

Progressive first-failure censoring is a flexible and cost-efficient strategy that captures real-world testing scenarios where only the first failure is observed at each stage while randomly removing remaining units, making it ideal for biomedical and reliability studies. By applying the $\alpha$-power transformation to the exponential baseline, the proposed model introduces an additional flexibility parameter that enriches the family of lifetime distributions, enabling it to better capture varying failure rates and diverse hazard rate behaviors commonly observed in biomedical data, thus extending the classical exponential model. This study develops a novel computational framework for analyzing an $\alpha$-powered exponential model under beta-binomial random removals within the proposed censoring test. To address the inherent complexity of the likelihood function arising from simultaneous random removals and progressive censoring, we derive closed-form expressions for the likelihood, survival, and hazard functions and propose efficient estimation strategies based on both maximum likelihood and Bayesian inference. For the Bayesian approach, gamma and beta priors are adopted, and a tailored Metropolis–Hastings algorithm is implemented to approximate posterior distributions under symmetric and asymmetric loss functions. To evaluate the empirical performance of the proposed estimators, extensive Monte Carlo simulations are conducted, examining bias, mean squared error, and credible interval coverage under varying censoring levels and removal probabilities. Furthermore, the practical utility of the model is illustrated through three oncological datasets, including multiple myeloma, lung cancer, and breast cancer patients, demonstrating superior goodness of fit and predictive reliability compared to traditional models. The results show that the proposed lifespan model, under the beta-binomial probability law and within the examined censoring mechanism, offers a flexible and computationally tractable framework for reliability and biomedical survival analysis, providing new insights into censored data structures with random withdrawals. Full article

Accurate modeling of product lifetimes is vital in reliability analysis and engineering to ensure quality and maintain competitiveness. This paper proposes the progressively randomly censored Maxwell distribution, which incorporates both progressive Type-II and random censoring within the Maxwell distribution framework. The model allows for the planned removal of surviving units at specific stages of an experiment, accounting for both deliberate and random censoring events. It is assumed that survival and censoring times each follow a Maxwell distribution, though with distinct parameters. Both frequentist and Bayesian approaches are employed to estimate the model parameters. In the frequentist approach, maximum likelihood estimators and their corresponding confidence intervals are derived. In the Bayesian approach, Bayes estimators are obtained using an inverse gamma prior and evaluated through a Markov Chain Monte Carlo (MCMC) method under the squared error loss function (SELF). A Monte Carlo simulation study evaluates the performance of the proposed estimators. The practical relevance of the methodology is demonstrated using a real data set. Full article

The Gumbel Type-II distribution is a widely recognized and frequently utilized lifetime distribution, playing a crucial role in reliability engineering. This paper focuses on the statistical inference of the Gumbel Type-II distribution under a random censoring scheme. From a frequentist perspective, point estimates for the unknown parameters are derived using the maximum likelihood estimation method, and confidence intervals are constructed based on the Fisher information matrix. From a Bayesian perspective, Bayes estimates of the parameters are obtained using the Markov Chain Monte Carlo method, and the average lengths of credible intervals are calculated. The Bayesian inference is performed under both the squared error loss function and the general entropy loss function. Additionally, a numerical simulation is conducted to evaluate the performance of the proposed methods. To demonstrate their practical applicability, a real world example is provided, illustrating the application and development of these inference techniques. In conclusion, the Bayesian method appears to outperform other approaches, although each method offers unique advantages. Full article

Background/Objectives: School-based caries prevention can increase access to critical dental services and reduce oral health inequities. However, little is known regarding the incidence of dental caries in children participating in school caries prevention, and caries diagnosis is often interval censored. Methods: In this paper, we used data from a longitudinal, school-based, randomized clinical trial of minimally invasive treatments for dental caries to estimate the per-visit incidence rate and compare the hazard of dental caries in children receiving either silver diamine fluoride or glass ionomer dental sealants. To account for interval censoring, we used semiparametric transformation models for univariate failure time data and imputed caries incidence using G-imputation. Results: There were 3040 children that met inclusion criteria for analysis, 1516 (49.9%) of which were randomly assigned to receive silver diamine fluoride and 1524 (50.1%) were assigned to receive glass ionomer dental sealants and atraumatic restorations. There were no differences in the hazard of caries between treatments (HR = 0.99, 95% CI = 0.72, 1.24), while children with caries at baseline had a significant increase in the hazard of new caries (HR = 2.54, 95% CI = 2.26, 2.83) compared to those that were caries free. The per-visit caries incidence ranged from 4.8 to 11.1 at the individual level and increased with each successive study observation. Conclusions: School-based caries prevention can positively affect caries incidence, and the results can be used to inform future program design and implementation. Full article

In this paper, we investigate the inferential procedures within both classical and Bayesian frameworks for the generalized logistic distribution under a random censoring model. For randomly censored data, our main goals were to develop maximum likelihood estimators and construct confidence intervals using the Fisher information matrix for the unknown parameters. Additionally, we developed Bayes estimators with gamma priors, addressing both squared error and general entropy loss functions. We also calculated Bayesian credible intervals for the parameters. These methods were applied to two real datasets with random censoring to provide valuable insights. Finally, we conducted a simulation analysis to assess the effectiveness of the estimated values. Full article

This work focuses on making Bayesian inferences for the two-parameter Birnbaum–Saunders (BS) distribution in the presence of right-censored data. A flexible Gibbs sampler is employed to handle the censored BS data in this Bayesian work that relies on Jeffrey’s and Achcar’s reference priors. A comprehensive simulation study is conducted to compare estimates under various parameter settings, sample sizes, and levels of censoring. Further comparisons are drawn with real-world examples involving Type-II, progressively Type-II, and randomly right-censored data. The study concludes that the suggested Gibbs sampler enhances the accuracy of Bayesian inferences, and both the amount of censoring and the sample size are identified as influential factors in such analyses. Full article

In this research, random censoring is employed as a methodology for parameter estimation within the context of an exponential distribution. These parameter estimations are conducted using both the Bayesian and maximum likelihood approaches. In the Bayesian framework, Lindley’s approximation method is applied to derive estimates, which are subsequently assessed under three distinct balanced loss functions. To gauge the efficacy of different estimation techniques, simulation-based investigations are conducted. Additionally, a real-world data analysis is executed to illustrate the practical applicability of these methodologies. The findings consistently underscore the superiority of Bayesian parameter estimates in comparison with their maximum likelihood counterparts across all analyzed methodologies. Full article

In this article, we present a Markov Bernoulli Lomax (MB-L) model, which is obtained by a countable mixture of Markov Bernoulli and Lomax distributions, with decreasing and unimodal hazard rate function (HRF). The new model contains Marshall- Olkin Lomax and Lomax distributions as a special case. The mathematical properties, as behavior of probability density function (PDF), HRF, r^th moments, moment generating function (MGF) and minimum (maximum) Markov-Bernoulli Geometric (MBG) stable are studied. Moreover, the estimates of the model parameters by maximum likelihood are obtained. The maximum likelihood estimation (MLE), bias and mean squared error (MSE) of MB-L parameters are inspected by simulation study. Finally, a MB-L distribution was fitted to the randomly censored and COVID-19 (complete) data. Full article

The purpose of this study was to examine the effect of cognitive training on the risk of experiencing a fall across 10 years. The study used data from the Advanced Cognitive Training for Independent and Vital Elderly (ACTIVE) randomized controlled trial. Older adults aged 65–94 were randomly assigned to speed of processing, memory, or reasoning training or to a no-contact control group (n = 2802). The experience of a fall in the prior two months was assessed at baseline and at 1, 2, 3, 5, and 10 years posttest. Cox proportional hazards explored group differences in the total sample, as well as group differences for participants classified as low risk (n = 2360) and high risk (n = 442) for future falls. The data were censored at the first reported fall postbaseline. After baseline, 983 (35.08%) participants across the full sample reported a fall. There were no significant effects of the training in the full sample or in the low-risk sample of participants. However, the participants at greater risk for future falls in the speed of processing training group were 31% less likely (HR = 0.69; 95% CI = 0.48, 0.998, p = 0.049) to experience a subsequent fall across ten years compared to the control group. Reasoning and memory training did not reduce a future fall in the high-risk sample. The speed of processing training reduced the risk of future falls across ten years in the high-risk participants. Future work should examine moderators and mediators of training in at-risk samples. Full article