Search

The two-parameter Rayleigh distribution, as an extended distribution of the Rayleigh distribution, has been widely applied in reliability analysis. With the introduction of the location parameter, two-parameter Rayleigh distribution becomes more flexible in fitting real-data. In this paper, based on generalized progressively hybrid censored(GPHC) sample from the two-parameter Rayleigh distribution, Classical and Bayesian inferences are discussed. The Newton-Raphson(NR) and Expectation-Maximization(EM) algorithms are used to compute the maximum likelihood estimates(MLEs). As well as the asymptotic confidence interval(ACI) estimation is obtained through the asymptotic distribution theory of maximum likelihood estimation(MLE) and computation of the observed Fisher information matrix. In Bayesian frame, the estimation of unknown parameters and prediction of future observable are taken into consideration. Due to Bayesian estimation is challenging to compute precisely and for the purpose of comparison, the Lindley's approximation, the Tierney-Kadane(TK) approximation and Markov chain Monte Carlo(MCMC) method are employed to obtain Bayesian estimates. Then, combining the MCMC algorithm mentioned in the article, the one- and two- samples Bayesian prediction are obtained. Finally, the simulation results are provided and a real-life data set is used for illustration purpose. [ABSTRACT FROM AUTHOR]

In this paper, statistical inference of an inverted exponentiated Rayleigh model is studied when the failure times are obtained under a modified progressive hybrid censoring. The maximum likelihood estimators of the model parameters together with associated existence and uniqueness are established, and approximate confidence intervals are constructed based on asymptotic theory. Alternatively, generalized point and interval estimates for unknown parameters are also constructed based on the proposed pivotal quantities for comparison. In addition, predictive intervals of remaining useful life from the inverted exponentiated Rayleigh distribution are also constructed under classical and generalized inferential approaches, respectively. Finally, extensive simulation studies are carried out to compare the performance of the proposed methods, and two real-life examples are analyzed for illustration. The numerical results indicate that both traditional likelihood and generalized inferential methods work satisfactorily, and that our proposed generalized approach appears much more appealing and are superior to classical results. [ABSTRACT FROM AUTHOR]

Competing risks data frequently appear in real-world operations like quality inspections, survival analysis, reliability tests, and clinical trials. From the quality point of view, relative risk rate can be considered an interesting quality indicator in analyzing the competing risks data for statistical process monitoring purposes. The relative risk rate measures the proportion of failures caused by the primary risk among a set of competing risks. This paper introduces two Shewhart-type control charts for monitoring the relative risk rate when the lifetimes of competing risks are independent Weibull random variables. The former chart is constructed based on the maximum likelihood estimation method, while the latter is developed based on the Bayesian approach. The proposed control charts can be applied in Phase II. The calculation of the Bayesian control charts and the evaluation of both process monitoring techniques have been done based on Monte Carlo simulations. The performance of the proposed control charts has been examined based on the average run length metric. The illustrative example is also discussed in detail to demonstrate the applicability of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the stress-strength reliability estimation under balanced joint Type-II progressive censoring scheme for independent samples from two different populations. We simultaneously place two independent samples where the experimental units follow Weibull distributions with common shape parameter β and different scale parameters α, λ, respectively. The maximum likelihood estimators of the unknown parameters are derived. Further, the Bayesian inference is considered using Lindley's approximation and Gibbs sampling method. Extensive simulations are performed to see the effectiveness of the proposed estimation methods. Further, we derive the optimal censoring scheme in the Bayesian framework by using the variable neighbourhood search method proposed by [Bhattacharya et al. On optimum life-testing plans under type-ii progressive censoring scheme using variable neighbourhood search algorithm. Test. 2016;25(2):309–330]. Further, some simulation schemes are provided to compare the performances of the estimations under the jointly censored samples versus two separate censored samples. [ABSTRACT FROM AUTHOR]

In this paper, a unit inverse Weibull distribution as well as its basic structural properties is proposed. Furthermore, classical inferences for multicomponent reliability are discussed under type-II censoring when stress and strength components have a common parameter. The maximum likelihood estimator of the reliability is obtained and in sequel an asymptotic interval is constructed. Pivotal quantities are constructed and then generalized point and interval estimators are obtained for the reliability. Likelihood and pivotal quantities-based estimations are presented when all parameters are unequal as well. The performance of different estimators is investigated using simulation studies and real-life examples are studied from an application viewpoint. Finally, some concluding remarks are given. [ABSTRACT FROM AUTHOR]

In this paper, interval estimation of the two-parameter exponential distribution based on constant-stress accelerated life test data under Type-II censoring is studied. The life-stress models of the scale and location parameters are assumed to be log-linear. The maximum likelihood estimators of the model parameters are obtained. The exact and approximate confidence intervals for the parameters in the life-stress model of the scale parameter are developed. The generalized confidence intervals for the parameters in the life-stress model of the location parameter, and mean and reliability function at the designed stress level are derived. The performance of the proposed generalized confidence intervals is assessed by the Monte Carlo simulation. Finally, a real example is used to illustrate our methods. [ABSTRACT FROM AUTHOR]

Estimation of causal treatment effects has attracted a great deal of interest in many areas including social, biological and health science, and for this, instrumental variable (IV) has become a commonly used tool in the presence of unmeasured confounding. In particular, many IV methods have been developed for right-censored time-to-event outcomes. In this paper, we consider a much more complicated situation where one faces interval-censored time-to-event outcomes, which are ubiquitously present in studies with, for example, intermittent follow-up but are challenging to handle in terms of both theory and computation. A sieve maximum likelihood estimation procedure is proposed for estimating complier causal treatment effects under the additive hazards model, and the resulting estimators are shown to be consistent and asymptotically normal. A simulation study is conducted to evaluate the finite sample performance of the proposed approach and suggests that it works well in practice. It is applied to a breast cancer screening study. [ABSTRACT FROM AUTHOR]

In this paper, we consider a transformation in a random variable which follows a bimodal Birnbaum-Saunders distribution. We propose the unit-bimodal Birnbaum-Saunders (UBBS) distribution and investigate some of its important properties, like cumulative distribution function, moments, survival function and risk function. We apply the UBBS distribution to censored data inflated at zero and one. We used the maximum likelihood approach for parameter estimation and to compare the models. Given the flexibility in UBBS distribution modes, our proposal performs best in beta regression models with zero and/or one excess. [ABSTRACT FROM AUTHOR]

A single-parameter Pareto model, Pareto I, arises in many areas of application such as pricing of insurance risks, measuring income or wealth inequality in economics, or modelling lengths of telephone calls in telecommunications. In insurance, for example, it is common to work with data that are truncated (due to deductibles), censored (due to policy limits), and contaminated by outliers (due to model misspecification). Therefore, it is prudent to estimate Pareto I using robust procedures that are designed for such data transformations and are resistant to outliers. In this paper, we consider trimmed (T) and winsorized (W) estimators for the Pareto tail index α, and conduct a simulation study to check these estimators' performance in finite samples. Two broad aspects are investigated: Convergence of α ˆ 's to α as sample size increases from n = 25 to n = 1000. This is evaluated by presenting a series of boxplots and measuring each estimator's relative bias and finite-sample relative efficiency (with respect to the asymptotic variance of the maximum likelihood estimator, MLE). Sensitivity of α ˆ 's and of two value-at-risk estimates to a new observation (an outlier) that is placed at various locations within the sample ranging from the point of left-truncation/-censoring to the point of right-censoring. We find that with respect to (a), T- and W-estimators perform best when n is small and MLE outperforms its competitors when n is large. And with respect to (b), MLE is not robust whilst T's and W's can offer any desired degree of robustness. [ABSTRACT FROM AUTHOR]

The generalised maximum likelihood estimator (GMLE) of a survival function S o (t) based on truncated interval-censored (TIC) data has been studied since 1990s (by Frydman, H. (1994), 'A note on nonparametric estimation of the distribution function from interval censored and truncated data', Journal of the Royal Statistical Society, Series B, 56, 71–74 among others). In the literature related to the GMLE based on TIC data, there are several issues that have not been properly settled in both methodology and theory including: (1) innermost intervals based on the TIC data are not correctly formulated and they lead to inconsistent estimators which are not the GMLE; and (2) the consistency of the GMLE has not been established. We settle these two issues in this paper. In particular, we specify the correct forms of innermost intervals and establish consistency results for the GMLE under a realistic model. [ABSTRACT FROM AUTHOR]

The aim of the paper is to estimate the unknown parameters of weighted exponential distribution based on the competing risks model under progressively Type-II censoring. It is supposed that the latent causes of failures have weighted exponential distributions with different parameters. The maximum likelihood estimations of four unknown parameters are derived and the uniqueness and existence of them are theoretically proved. Moreover, approximate intervals are proposed and constructed with the delta method and Fisher information matrix. Bootstrap methods are also applied to calculate the confidence intervals. Furthermore, Bayes estimates and the corresponding credible intervals under three various loss functions are computed by using the Monte Carlo Markov Chain method. A simulation study is conducted to assess the statistical performance of all the estimators. Ultimately, real data analysis is provided to illustrate all the statistical inferential procedures developed in the paper. [ABSTRACT FROM AUTHOR]

In this paper, we study the sparse estimation under the semiparametric linear transformation models for the current status data, also called type I interval-censored data. For the problem, the failure time of interest may be dependent on the censoring time and the association parameter between them is left unspecified. To address this, we employ the copula model to describe the dependence between them and a two-stage estimation procedure to estimate both the association parameter and the regression parameter. In addition, we propose a penalized maximum likelihood estimation procedure based on the broken adaptive ridge regression, and Bernstein polynomials are used to approximate the nonparametric functions involved. The oracle property of the proposed method is established and the numerical studies suggest that the method works well for practical situations. Finally, the method is applied to an Alzheimer's disease study that motivated this investigation. [ABSTRACT FROM AUTHOR]

Gompertz distribution is a significant and commonly used lifetime distribution, which plays an important role in reliability engineering. In this paper, we study the statistical inference of Gompertz distribution based on adaptive Type-II hybrid progressive censored schemes. From the perspective of frequentist, we derive the point estimations through the method of maximum likelihood estimation (MLE) and the existence of MLE is proved. Besides MLE, we propose the stochastic EM algorithm to reduce complexity and simplify computing. We also apply the method of Bootstraps (Bootstrap-p and Bootstrap-t) to construct confidence intervals. From Bayesian aspect, the Bayes estimates of the unknown parameters are evaluated by applying the MCMC method, the average length and coverage rate of credible intervals are also carried out. The Bayes inference is based on the squared error loss function and LINEX loss function. Furthermore, a numerical simulation is conducted to assess the performance of the proposed methods. Finally, a real-life example is considered to illustrate the application and development of the inference methods. In summary, the Bayesian method seems to perform the best among all approaches, while other approaches also present different advantages. [ABSTRACT FROM AUTHOR]

In this paper, the Bayesian and non-Bayesian estimation of $$\psi = P(X \gt Y)$$ ψ = P (X > Y) based on the progressively first-failure censored data is considered. The $$X$$ X and $$Y$$ Y are strength and stress random variables and follow the Topp-Leone distributions, respectively. The maximum likelihood and Bayes estimators of $$\psi $$ ψ are derived. The Bayes estimators under generalized entropy loss function are computed using Lindley's approximation and Gibbs sampling methods. Different interval estimates like asymptotic, bootstrap confidence, Bayesian credible, and highest posterior density credible intervals of $$\psi $$ ψ are constructed. Furthermore, a Monte Carlo numerical study is conducted to check the performance of various estimators developed. Finally, an application of algorithm real data is considered for illustrative purposes. [ABSTRACT FROM AUTHOR]

We, in this paper, focus on the inference of conditional quantile difference (CQD) for left-truncated and right-censored model. Based on local conditional likelihood function of the observed data, local likelihood ratio function and smoothed local log-likelihood ratio (log-SLL) of the CQD are constructed, and the maximum local likelihood estimator of the CQD is further defined from the log-SLL. When the observations are assumed to be a sequence of stationary α-mixing random variables, we establish asymptotic normality of the defined estimator, and prove the Wilks' theorem of adjusted log-SLL. Besides, we define another estimator of the CQD based on product-limit estimator of conditional distribution function and give its asymptotic normality. Also, simulation study and real data analysis are conducted to investigate the finite sample behaviour of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper is an effort to obtain the point estimators and interval estimators for the unknown parameters, reliability and hazard rate functions of bathtub-shaped distribution based on generalized progressive hybrid censoring. We first derive the maximum likelihood estimators for the quantities and compute the estimates using Newton iterative method. Observed Fisher's information matrix is obtained and then the asymptotic confidence intervals are constructed. Besides, two bootstrap confidence intervals are proposed for the quantities. The Bayesian estimators are acquired under squared error loss function using Lindley method and Metropolis-Hastings method with Gibbs sampling, and Bayesian credible intervals are constructed based on Markov Chain Monte Carlo (MCMC) samples as well. Finally, extensive simulation studies are conducted to compare the performance of the estimators and a real data set is analyzed for illustrative purpose. [ABSTRACT FROM AUTHOR]

In this paper, we first develop exact likelihood inference for Laplace distribution based on a generalized Type-I hybrid censored sample (Type-I HCS). We derive explicit expressions for the maximum likelihood estimators (MLEs) of the location and scale parameters. We then derive the joint moment generating function (MGF) of the MLEs, and use it to obtain the exact distributions and moments of the MLEs. Using an analogous approach, we extend the results to a generalized Type-II hybrid censored sample (Type-II HCS) next. Finally, we present a numerical example to illustrate all the results established here. [ABSTRACT FROM AUTHOR]

The consistency of the semi-parametric maximum likelihood estimator (SMLE) under the semi-parametric linear regression model with right-censoring data (SPLRRC model) has not been studied under the necessary and sufficient condition for the identifiability of the parameters. In this paper, we discuss the necessary and sufficient condition for the consistency of SMLE under type I right censoring. [ABSTRACT FROM AUTHOR]

This paper introduces a new class of distributions by compounding the inverse Lindley distribution and power series distributions which is called compound inverse Lindley power series (CILPS) distributions. An important feature of this distribution is that the lifetime of the component associated with a particular risk is not observable, rather only the minimum lifetime value among all risks is observable. Further, these distributions exhibit an unimodal failure rate. Various properties of the distribution are derived. Besides, two special models of the new family are investigated. The model parameters of the two sub-models of the new family are obtained by the methods of maximum likelihood, least square, weighted least square and maximum product of spacing and compared them using the Monte Carlo simulation study. Besides, the log compound inverse Lindley regression model for censored data is proposed. Three real data sets are analyzed to illustrate the flexibility and importance of the proposed models. [ABSTRACT FROM AUTHOR]

This paper deals with the statistical inference of the unknown parameters of three-parameter exponentiated power Lindley distribution under adaptive progressive type-II censored samples. The maximum likelihood estimator (MLE) cannot be expressed explicitly, hence approximate MLEs are conducted using the Newton–Raphson method. Bayesian estimation is studied and the Markov Chain Monte Carlo method is used for computing the Bayes estimation. For Bayesian estimation, we consider two loss functions, namely: squared error and linear exponential (LINEX) loss functions, furthermore, we perform asymptotic confidence intervals and the credible intervals for the unknown parameters. A comparison between Bayes estimation and the MLE is observed using simulation analysis and we perform an optimally criterion for some suggested censoring schemes by minimizing bias and mean square error for the point estimation of the parameters. Finally, a real data example is used for the illustration of the goodness of fit for this model. [ABSTRACT FROM AUTHOR]

The joint censoring scheme is of great importance when the motive of study is to compare the relative merits of products in relation of their service times. In last few years, progressive censoring received considerable attention in order to save cost and time of the experiment. This paper deals with inferences for Lindley populations, when joint progressive type-II censoring scheme is applied on two samples in a joint manner. Here, the maximum likelihood estimators of parameters are derived along with their associated confidence intervals which are dependent on the Fisher's information matrix. The boot-p and boot-t confidence intervals are also obtained. Bayes estimators of the unknown parameters assuming gamma priors are calculated. The concept of importance sampling technique and Gibbs sampling technique are used as the Bayes estimators cannot be calculated in closed form. HPD credible intervals are also constructed. A Monte Carlo simulation study is performed to measure the efficiency of the estimates. A real data set is given for illustrative purpose. Finally some criteria for an optimum censoring scheme are discussed. [ABSTRACT FROM AUTHOR]

In this paper, inference for a competing risks model is studied when latent failure times follow Kumaraswamy distribution and causes of failure are partially observed. Under generalized progressive hybrid censoring, existence and uniqueness of maximum likelihood estimators of model parameters are established. The confidence intervals are obtained by using asymptotic distribution theory. We further compute Bayes estimators along with credible intervals. In addition, inference is also discussed when there is order restricted shape parameters. The performance of all estimates is investigated using Monte-Carlo simulations. Finally, analysis of a real data set is presented for illustration purposes. [ABSTRACT FROM AUTHOR]

In many practical problems relate to progressively Type-II censored sampling plans, not only an experiment process determines inevitably to use random removals but also a fixed removals assumption may be cumbersome to analyze some results of statistical inference. This paper investigates the estimation problem when lifetimes are the two-parameter Lindley distributed and are collected under two removal patterns based on the uniform discrete distribution and the binomial distribution. The maximum likelihood estimations (MLEs) of parameters are obtained by a derivative-free optimization method and without applying the logarithm of the likelihood function. Furthermore, we propose a method for starting values of optimization to obtain the MLEs and compare numerically their bias, variance, covariance and mean squared error under the two different removal plans. Then, the expected times are discussed and compared numerically under the two approaches of generating random removals. Finally, the optimal progressive Type-II censoring scheme is provided based on the measure of the smallest expected experiment time. [ABSTRACT FROM AUTHOR]

The censored exponential regression model is commonly used for modeling lifetime data. In this paper, we derive a simple matrix formula for the second-order covariance matrix of the maximum likelihood estimators in this class of regression models. The general matrix formula covers many types of censoring commonly encountered in practice. Also, the formula only involves simple operations on matrices and hence is quite suitable for computer implementation. Monte Carlo simulations are provided to show that the second-order covariances can be quite pronounced in small to moderate sample sizes. Additionally, based on the second-order covariance matrix, we propose an alternative Wald statistic to test hypotheses in this class of regression models. Monte Carlo simulation experiments reveal that the alternative Wald test exhibits type I error probability closer to the chosen nominal level. We also present an empirical application for illustrative purposes. [ABSTRACT FROM AUTHOR]

In this paper, we study an algorithm to compute the non-parametric maximum likelihood estimator of stochastically ordered survival functions from case 2 interval-censored data. The algorithm, simply denoted by SQP (sequential quadratic programming), re-parameterizes the likelihood function to make the order constraints as a set of linear constraints, approximates the log-likelihood function as a quadratic function, and updates the estimate by solving a quadratic programming. We particularly consider two stochastic orderings, simple and uniform orderings, although the algorithm can also be applied to many other stochastic orderings. We illustrate the algorithm using the breast cancer data reported in Finkelstein and Wolfe (1985). [ABSTRACT FROM AUTHOR]

In this paper, based on hybrid censored sample from a two parameter exponentiated half logistic distribution, we consider the problem of estimating the unknown parameters using frequentist and Bayesian approaches. Expectation-Maximization, Lindley's approximation and Metropolis-Hastings algorithms are used for obtaining point estimators and corresponding confidence intervals for the shape and scale parameters involved in the underlying model. Data analyses involving the survival times of patients suffering from cancer diseases and treated radiotherapy and/or chemotherapy have been performed. Finally, numerical simulation study was conducted to assess the performances of the so developed methods and conclusions on our findings are reported. [ABSTRACT FROM AUTHOR]

Multicollinearity is often ignored in censored regression model. In this respect, Tobit Liu estimation is proposed as an alternative in order to dispel the adverse effects of multicollinearity on the maximum likelihood estimation. Tobit Liu estimator is compared with Tobit ridge estimator and Tobit maximum likelihood estimator, theoretically via mean square error. For empirical analysis, we prefer Mroz dataset which is a phenomenon in the context of censored regression. Since many studies have investigated Mroz dataset by neglecting multicollinearity, we handle this dataset in the context of multicollinearity in this paper. Moreover, it is seen that multicollinearity is not included in pioneer studies' simulation designs. Therefore, we conduct a Monte Carlo simulation study where we take account of different levels of multicollinearity while generating data. Briefly, this study contributes to filling an important gap in the literature and proposes to investigate other econometrically censored data in the context of multicollinearity. [ABSTRACT FROM AUTHOR]

In the current paper, the maximum likelihood and Bayes estimators for the two shape parameters of the Burr Type III distribution are investigated based on adaptive Type II progressive hybrid censored data. The maximum likelihood estimators are provided for estimating the unknown parameters. The existence and uniqueness of the maximum likelihood estimation are shown using the graphical method. The Bayes estimates are obtained under two loss functions using the Lindley's method and Metropolis-Hastings sampling procedure. Further, approximate and Bayesian intervals are constructed. Monte Carlo simulation study is performed to check the accuracy of the estimates and compare the performance of the proposed confidence intervals. Also, the nano droplet data is analyzed to illustrate the application and development of the inference methods. [ABSTRACT FROM AUTHOR]

The inverse generalized gamma (IGG) distribution can be particularly useful for modelling reliability (survival) data with an upside-down bathtub hazard rate function. The mathematical properties and estimation methods are not known in the literature. In this paper, we provide Bayesian inferences for the IGG distribution parameters using non-informative priors, namely, the Jeffreys prior and the reference prior. Extensive numerical simulations are conducted to investigate the performance of the proposed estimation method when compared with the classical inference. Finally, the potentiality of the IGG model is analysed by employing real environmental data. [ABSTRACT FROM AUTHOR]

In this paper, we study the performance of a soccer player based on analysing an incomplete data set. To achieve this aim, we fit the bivariate Rayleigh distribution to the soccer dataset by the maximum likelihood method. In this way, the missing data and right censoring problems, that usually happen in such studies, are considered. Our aim is to inference about the performance of a soccer player by considering the stress and strength components. The first goal of the player of interest in a match is assumed as the stress component and the second goal of the match is assumed as the strength component. We propose some methods to overcome incomplete data problem and we use these methods to inference about the performance of a soccer player. [ABSTRACT FROM AUTHOR]

In this paper, we derive a new continuous-discrete mixture regression model which is useful for describing highly censored data. This mixture model employs the Birnbaum-Saunders distribution for the continuous response variable of interest, whereas the Bernoulli distribution is used for the point mass of the censoring observations. We estimate the corresponding parameters with the maximum likelihood method. Numerical evaluation of the model is performed by means of Monte Carlo simulations and of an illustration with real data. The results show the good performance of the proposed model, making it an addition to the tool-kit of biometricians, medical doctors, applied statisticians, and data scientists. [ABSTRACT FROM AUTHOR]

In this paper, we propose a bimodal gamma distribution using a quadratic transformation based on the alpha-skew-normal model. We discuss several properties of this distribution such as mean, variance, moments, hazard rate and entropy measures. Further, we propose a new regression model with censored data based on the bimodal gamma distribution. This regression model can be very useful to the analysis of real data and could give more realistic fits than other special regression models. Monte Carlo simulations were performed to check the bias in the maximum likelihood estimation. The proposed models are applied to two real data sets found in the literature. [ABSTRACT FROM AUTHOR]

The copula approach is a way to describe the dependence structure between variables. This could be done through splitting the analysis of the joint distribution of a multivariate random vector into two parts: the analysis of the marginals and the analysis of a copula which describes the dependence structure. An important field of reliability in which the copula approach could be applied, is the accelerated life testing (ALT). When a test unit fails under ALT, there are often more than one fatal cause for the failure. In this paper, we consider the simple step-stress ALT (SSALT) under type II censoring when the lifetime distribution of the different risks are dependent. The dependence structure between the competing risks is described using the copula approach. The point estimates of the unknown parameters are obtained using the maximum likelihood method. Also, the interval estimates for the unknown parameters are constructed using the asymptotic distributions and the parametric bootstrap method. Numerical analysis including simulated data and a real life data set is conducted to study the performance of the estimates. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the problem of predicting times to the latent failures of units censored in multiple stages in a progressively Type-II censored competing risks model. It is assumed that the lifetime distribution of the latent failure times are independent and exponential-distributed with the different scale parameters. Several classical point predictors such as the maximum likelihood predictor, the best unbiased predictor, the best linear unbiased predictor, the median unbiased predictor and the conditional median predictor are obtained. The Bayesian point predictors are derived under squared error loss criterion. Moreover, the point estimators of the unknown parameters are obtained using the observed data and different point predictors of the latent failure times. Finally, Monte-Carlo simulations are carried out to compare the performances of the different methods of prediction and estimation and one real data is used to illustrate the proposed procedures. [ABSTRACT FROM AUTHOR]

In this paper, we extend the censored linear regression model with normal errors to Student-terrors. A simple EM-type algorithm for iteratively computing maximum-likelihood estimates of the parameters is presented. To examine the performance of the proposed model, case-deletion and local influence techniques are developed to show its robust aspect against outlying and influential observations. This is done by the analysis of the sensitivity of the EM estimates under some usual perturbation schemes in the model or data and by inspecting some proposed diagnostic graphics. The efficacy of the method is verified through the analysis of simulated data sets and modelling a real data set first analysed under normal errors. The proposed algorithm and methods are implemented in the R packageCensRegMod. [ABSTRACT FROM AUTHOR]

Inverse Weibull (IW) distribution is widely used due to its non-monotonic hazard function. For the IW distribution, existing research on statistical inference has mostly focused on censored data, but there has been no study on multiply Type-I censoring until now as far as we know. The multiple Type-I censoring, acted as an extended form of Type-I censoring, is frequently encountered in industry and medicine research, which also needs to be paid attention. Thus, this study conducts detailed analyses on the reliability of IW distribution with multiply Type-I censored data, including point estimation and confidence interval (CI) construction. Four methods, including the maximum likelihood estimation (MLE), least square estimation (LSE), and two Bayesian estimations, namely MCMC and Lindley, are adopted in point estimation. Results show that the Lindley method performs best with small mission times, while MLE is optimal for large mission times. Specifically, for the CIs construction, we proposed a pivotal quantity based on LSE to construct the CIs of reliability and compare it with two popular methods, Fisher information matrix (FIM) derivation and MCMC algorithm. Our proposed method shows competitive performance as the MCMC and outperforms FIM. Finally, those estimation methods are applied to an example for illustration. [ABSTRACT FROM AUTHOR]

Interval-censored data arise when a failure time say,Tcannot be observed directly but can only be determined to lie in an interval obtained from a series of inspection times. The frequentist approach for analysing interval-censored data has been developed for some time now. It is very common due to unavailability of software in the field of biological, medical and reliability studies to simplify the interval censoring structure of the data into that of a more standard right censoring situation by imputing the midpoints of the censoring intervals. In this research paper, we apply the Bayesian approach by employing Lindley's 1980, and Tierney and Kadane 1986 numerical approximation procedures when the survival data under consideration are interval-censored. The Bayesian approach to interval-censored data has barely been discussed in literature. The essence of this study is to explore and promote the Bayesian methods when the survival data been analysed are is interval-censored. We have considered only a parametric approach by assuming that the survival data follow a loglogistic distribution model. We illustrate the proposed methods with two real data sets. A simulation study is also carried out to compare the performances of the methods. [ABSTRACT FROM AUTHOR]

Failure time data occur in many areas and in various censoring forms and many models have been proposed for their regression analysis such as the proportional hazards model and the proportional odds model. Another choice that has been discussed in the literature is a general class of semiparmetric transformation models, which include the two models above and many others as special cases. In this paper, we consider this class of models when one faces a general type of censored data, case K informatively interval-censored data, for which there does not seem to exist an established inference procedure. For the problem, we present a two-step estimation procedure that is quite flexible and can be easily implemented, and the consistency and asymptotic normality of the proposed estimators of regression parameters are established. In addition, an extensive simulation study is conducted and suggests that the proposed procedure works well for practical situations. An application is also provided. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to develop the approximate Bayes estimation of the five-dimensional vector of the parameters and reliability function of a mixture of two inverse Weibull distributions (MTIWD) under Type-2 censoring. Usually, the posterior distribution is complicated under the scheme of Type-2 censoring and the integrals that are involved cannot be obtained in a simple explicit form. In this study, we use Lindley's [Approximate Bayesian method, Trabajos Estadist. 31 (1980), pp. 223–237] approximate form of Bayes estimation in the case of an MTIWD under Type-2 censoring. Later, we calculate the estimated risks (ERs) of the Bayes estimates and compare them with the corresponding ERs of the maximum-likelihood estimates through Monte Carlo simulation. Finally, we analyse a real data set using the findings. [ABSTRACT FROM AUTHOR]

This paper addresses the estimation for the unknown scale parameter of the half-logistic distribution based on a Type-I progressively hybrid censoring scheme. We evaluate the maximum likelihood estimate (MLE) via numerical method, and EM algorithm, and also the approximate maximum likelihood estimate (AMLE). We use a modified acceptance rejection method to obtain the Bayes estimate and corresponding highest posterior confidence intervals. We perform Monte Carlo simulations to compare the performances of the different methods, and we analyze one dataset for illustrative purposes. [ABSTRACT FROM PUBLISHER]

This paper presents large-scale bending test, up to 19 m length, on glued laminated timber (GLT) beams with well-known beam setup and a model to predict the tensile strength of finger joint connections (FJ). Machine graded timber boards, with information about the dynamic stiffness and local knottiness were used to fabricate 12 GLT beams. The position of the timber boards were tracked throughout the GLT fabrication. To quantify the quality of the FJ additional FJ were fabricated and tested in tension. Based on the results, a model to predict their strength properties based on the grading information of the involved timber boards was developed using maximum likelihood estimation for censored data. [ABSTRACT FROM AUTHOR]

In this communication, various statistical inferential procedures for estimating unknown model parameters are investigated via utilizing partially observed dependent competing risks data under the unified hybrid censoring scheme when the latent failure times follow Marshall–Olkin bivariate Kumaraswamy distribution. The existence and uniqueness of the maximum likelihood estimators (MLEs) have been established. By using asymptotic normality property of MLE, the approximate confidence intervals have been constructed via observed Fisher information matrix. Moreover, Bayes estimates and the highest posterior density credible intervals have been computed under a highly flexible gamma-Dirichlet prior distribution by using Markov chain Monte Carlo technique. In addition, to compare the performance of proposed methods, a Monte Carlo simulation has been carried out. Finally, a real-life data set has been analysed to illustrate the operability and applicability of the methods considered. [ABSTRACT FROM AUTHOR]

Following the work of Chen and Bhattacharyya [Exact confidence bounds for an exponential parameter under hybrid censoring. Comm Statist Theory Methods. 1988;17:1857–1870], several results have been developed regarding the exact likelihood inference of exponential parameters based on different forms of censored samples. In this paper, the conditional maximum likelihood estimators (MLEs) of two exponential mean parameters are derived under joint generalized Type-I hybrid censoring on the two samples. The moment generating functions (MGFs) and the exact densities of the conditional MLEs are obtained, using which exact confidence intervals are then developed for the model parameters. We also derive the means, variances, and mean squared errors of these estimates. An efficient computational method is developed based on the joint MGF. Finally, an example is presented to illustrate the methods of inference developed here. [ABSTRACT FROM PUBLISHER]

This paper develops the Bayesian estimation for the Birnbaum–Saunders distribution based on Type-II censoring in the simple step stress–accelerated life test with power law accelerated form. Maximum likelihood estimates are obtained and Gibbs sampling procedure is used to get the Bayesian estimates for shape parameter of Birnbaum–Saunders distribution and parameters of power law–accelerated model. Asymptotic normality method and Markov Chain Monte Carlo method are employed to construct the corresponding confidence interval and highest posterior density interval at different confidence level, respectively. At last, the results are compared by using Monte Carlo simulations, and a numerical example is analyzed for illustration. [ABSTRACT FROM AUTHOR]

A progressive hybrid censoring scheme is a mixture of type-I and type-II progressive censoring schemes. In this paper, we mainly consider the analysis of progressive type-II hybrid-censored data when the lifetime distribution of the individual item is the normal and extreme value distributions. Since the maximum likelihood estimators (MLEs) of these parameters cannot be obtained in the closed form, we propose to use the expectation and maximization (EM) algorithm to compute the MLEs. Also, the Newton–Raphson method is used to estimate the model parameters. The asymptotic variance–covariance matrix of the MLEs under EM framework is obtained by Fisher information matrix using the missing information and asymptotic confidence intervals for the parameters are then constructed. This study will end up with comparing the two methods of estimation and the asymptotic confidence intervals of coverage probabilities corresponding to the missing information principle and the observed information matrix through a simulation study, illustrated examples and real data analysis. [ABSTRACT FROM PUBLISHER]

In this paper, we assume that the lifetimes have a two-parameter Pareto distribution and discuss some results of progressive Type-II censored sample. We obtain maximum likelihood estimators and Bayes estimators of the unknown parameters under squared error loss and a precautionary loss functions in progressively Type-II censored sample. Robust Bayes estimation of unknown parameters over three different classes of priors under progressively Type-II censored sample, squared error loss, and precautionary loss functions are obtained. We discuss estimation of unknown parameters on competing risks progressive Type-II censoring. Finally, we consider the problem of estimating the common scale parameter of two Pareto distributions when samples are progressively Type-II censored. [ABSTRACT FROM PUBLISHER]

In many practical situations, complete data are not available in lifetime studies. Many of the available observations are right censored giving survival information up to a noted time and not the exact failure times. This constitutes randomly censored data. In this paper, we consider Maxwell distribution as a survival time model. The censoring time is also assumed to follow a Maxwell distribution with a different parameter. Maximum likelihood estimators and confidence intervals for the parameters are derived with randomly censored data. Bayes estimators are also developed with inverted gamma priors and generalized entropy loss function. A Monte Carlo simulation study is performed to compare the developed estimation procedures. A real data example is given at the end of the study. [ABSTRACT FROM AUTHOR]

A general method for correcting the bias of the maximum likelihood estimator (MLE) of the common shape parameter of Weibull populations, allowing a general right censorship, is proposed in this paper. Extensive simulation results show that the new method is very effective in correcting the bias of the MLE, regardless of censoring mechanism, sample size, censoring proportion and number of populations involved. The method can be extended to more complicated Weibull models. [ABSTRACT FROM PUBLISHER]

In this paper, based on a jointly type-II censored sample from two exponential populations, the Bayesian inference for the two unknown parameters are developed with the use of squared-error, linear-exponential and general entropy loss functions. The problem of predicting the future failure times, both point and interval prediction, based on the observed joint type-II censored data, is also addressed from a Bayesian viewpoint. A Monte Carlo simulation study is conducted to compare the Bayesian estimators with the maximum likelihood estimator developed by Balakrishnan and Rasouli [Exact likelihood inference for two exponential populations under joint type-II censoring. Comput Stat Data Anal. 2008;52:2725–2738]. Finally, a numerical example is utilized for the purpose of illustration. [ABSTRACT FROM AUTHOR]

The Birnbaum–Saunders (BS) distribution is a positively skewed distribution and is a common model for analysing lifetime data. In this paper, we discuss the existence and uniqueness of the maximum likelihood estimates (MLEs) of the parameters of BS distribution based on Type-I, Type-II and hybrid censored samples. The line of proof is based on the monotonicity property of the likelihood function. We then describe the numerical iterative procedure for determining the MLEs of the parameters, and point out briefly some recently developed simple methods of estimation in the case of Type-II censoring. Some graphical illustrations of the approach are given for three real data from the reliability literature. Finally, for illustrative purpose, we also present an example in which the MLEs do not exist. [ABSTRACT FROM AUTHOR]