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The competing risks model plays an important role in the statistical analysis of engineering, econometric, biological and other fields. A tested product may fail from different causes. Therefore, these failure causes as if competing with each other to bring about the failure of tested products (an experimental unit). Hence, in the statistical literature, this is known as the competing risk problem and it has been studied quite extensively by several researchers when the lifetime of the product is the latent failure time of the first failure cause among all the possible failure causes. In this paper, a competing risks model based on a generalized progressive hybrid type-I (GPH type-I) censoring is considered when the latent lifetime distributions of failure causes are inverse Weibull (IW) distributed and partially observed. We established various estimation methods including Maximum likelihood estimates (MLEs) and Bayes estimates (BEs). MLEs with the corresponding asymptotic confidence intervals are obtained. Bayes estimates of the parameters are obtained based on squared error loss (SEL) function under the assumption of independent gamma priors. Furthermore, we applied Markov Chain Monte Carlo (MCMC) techniques to compute BEs and to calculate the credible intervals. Finally, simulation studies and real data set are used for illustrative purpose. [ABSTRACT FROM AUTHOR]

Mixture cure rate model for right censored survival data is considered in the present paper. We consider the case where the lifetime data follow the Weibull exponentiated exponential distribution. The model contains as special case the Weibull, exponentiated exponential and exponential mixture cure rate models. The paper utilizes the maximum likelihood method to estimate the parameters of the mixture cure rate model under the assumption of right censoring. Simulations study was performed in order to ascertain the performances of the MLE estimators of the mixture model. We generated random samples of different sizes from the model with some arbitrary values for the parameters for 5%, 10% and 15% cure fraction values. Bias and standard error were used as discrimination criteria. Finally, the application of the proposed methodology was demonstrated considering the Eastern Cooperative Oncology Group (ECOG) phase III clinical trial e1684 and the survival time of colorectal cancer patients from Malaysia. The proposed methodology was found to fits the e1684 data better than its sub-models. Furthermore, when compared with other competing long-term mixture cure models using the survival time of colorectal cancer data, the proposed methodology was also found to fit the data better than the models compared with. [ABSTRACT FROM AUTHOR]

There are many situations in reliability or medical studies, where items may fail due to one of several causes. Further, censoring is unavoidable in any life testing. In this paper attempts to estimate problem for the competing risks model where the data are adaptive type-II progressive hybrid censored scheme and follow the inverse Weibull distribution. In this regards, we obtain the maximum likelihood estimation of the parameters and the asymptotic confidence intervals for the unknown parameters. Further, Bayes estimates of the parameters which obtained based on squared error and LINEX loss functions under the assumptions of independent gamma priors. For Bayesian estimation, we take advantage of Markov Chain Monte Carlo techniques by applying the Metropolis-Hasting algorithm under the square error and LINEX loss function to derive Bayesian estimators. Finally, two data sets with a Monte Carlo simulation study and a real data set of the electronic applications are analyzed for illustrative purposes. [ABSTRACT FROM AUTHOR]

Reliability of the stress(Y) - strength(𝑋) R = P(Y > X) model using Bayesian estimation method is proposed in this paper. We used it to evaluate the component's performance when the two variables X and Y are independent Exponentiated q-Exponential random variables with common parameter 𝜆, 𝜀 and 𝜎. Three different loss functions [weighted, quadratic, and entropy] under two different prior functions [Gamma and Extension of Jeffery], with an empirical Bayes estimator for a type II censored sample are used. A comparison of the three reliability estimators for stress - strength are established with two different types of criteria such as mean squared error (MSE) and mean absolutely percentage error (MAPE). Finally, the results of the simulation study discovered that for small, medium, and large sample sizes, the entropy loss function, weighted and quadratic to the advantage, performed best, respectively. [ABSTRACT FROM AUTHOR]

In this paper, we attempt to supplement the distribution theory literature by incorporating a new bounded distribution, called the bounded exponentiated Weibull (BEW) distribution in the (0,1) intervals by transformation method. The proposed distribution exhibits decreasing, increasing, bathtub and right-skewed unimodal density while the hazard rate can have decreasing and bathtub shaped. Although our main focus is on the construction of chi-squared goodness-of-fit tests for the BEW distribution for right censored data based on Nikulin-Rao-Robson (NRR) statistic and its modification, in addition, we derive some basic statistical properties of the proposed BEW distribution. The test statistic used is the modified chi-squared statistic Y², developed by Bagdonavicius and Nikulin (2011) for some parametric models when data are censored. The performances of the proposed test is investigated through an extensive simulation study. An application to a real data set is also provided. The main purpose of this work is the construction of chisquared goodness of-fit tests for the transmuted generalized linear exponential distribution with unknown parameters and right censoring. The criterion test used is the modified chisquared statistic Y², developed by Bagdonavicius and Nikulin (2011) for some parametric models when data are censored. The performances of the proposed test is investigated through an extensive simulation study. An application to a real data set is also provided. [ABSTRACT FROM AUTHOR]

This paper addresses estimation of the shape parameter of the Topp-Leone distribution which is known for its applicability in lifetime data. For fixed scale parameter, four plug-in estimators are suggested to estimate the shape parameter. The properties of these estimators are examined and their performances against the maximum likelihood estimator (MLE) are evaluated for a range of the shape parameter values. Based on the second moment, an estimator, which has an algebraic solution, is derived. It turns out that this proposed estimator outperforms the estimator based on the first moment that has no algebraic solution. A plug-in estimator based on solving the estimation equation mapping the empirical joint distribution function to the joint distribution function of a random sample is also derived and proven to constantly outperform the maximum likelihood estimator for all values of the shape parameter. [ABSTRACT FROM AUTHOR]

In this paper, point and interval estimations under modified Weibull (MW)distribution have been studied based on progressive first-failure censored scheme. The Bayes estimates (BE'S) have been computed based on squared error (SE) and (Linex) loss functions and using Markov Chain Monte Carlo(MCMC) algorithm. Also, based on this censoring scheme, the interval estimation problem of the parameters of MW distribution have been studied. A Monte Carlo simulation study has been carried out to compare the performances of the different methods by computing the mean squared errors (MES'S). Finally, point and interval estimates for all parameters have been studied based on a real data set as an illustrative example. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to derive the predictive inference for future responses from the compound Rayleigh model based on censored samples. The predictive density for a single future response, ith future response, and m future responses are derived on the basis of a type II as well as doubly censored sample. Two numerical examples are considered to illustrate the results. First example deals with a real data set that represents the survival times of 46 patients given chemotherapy treatment. The second example is the doubly censored sample of the heart transplantation surgery patients. Both examples are utilized to illustrate the predictive results. The highest predictive density intervals are determined for a single future response. [ABSTRACT FROM AUTHOR]

In this study, we introduced a new model of progressive type-II censoring which is a general form of the flexible progressive censoring (FPC) scheme proposed by Bairamov and Parsi (2010) and we called this scheme as generalized flexible progressive type-II censoring (GFPC) scheme. We also study the distribution of the failure times under proposed scheme. In addition, a simulation algorithm for generating GFPC sample has been given. Finally, we present simulated test times under GFPC scheme and conclude the paper. [ABSTRACT FROM AUTHOR]

In this paper, a Bayesian framework is utilized in conjunction with an informative prior to derive the posterior density for the parameters and the predictive density for a single future response given a type II censored sample which follows the two-parameter half-normal model. Two numerical studies are considered where type II censored samples contain upper extreme values. At first, a simulation study is used to illustrate the predictive results for a future response. Secondly, a real data set represents the stress-rupture life of kevlar 49/epoxy strands, which are subjected to constant sustained pressure at the 90% stress level until all have failed, is utilized to illustrate the results. Additionally, the summary results of the posterior parameters under the trim samples are given by using the Markov chain Monte Carlo method. The findings will be helpful to produce valid predictive inference when type II censored sample carries upper extremes. [ABSTRACT FROM AUTHOR]