Arnab Koley

Bio: Arnab Koley is an academic researcher from Indian Institute of Management Indore. The author has contributed to research in topic(s): Exponential distribution & Estimator. The author has an hindex of 3, co-authored 9 publication(s) receiving 30 citation(s). Previous affiliations of Arnab Koley include Indian Institute of Technology Kanpur.

On generalized progressive hybrid censoring in presence of competing risks

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

Analysis of Type-II hybrid censored competing risks data

Abstract: Kundu and Gupta [Analysis of hybrid life-tests in presence of competing risks. Metrica. 2007;65:159–170] provided the analysis of Type-I hybrid censored competing risks data, when the lifetime dist...

Interval Estimation of the Unknown Exponential Parameter Based on Time Truncated Data

Abstract: In this paper we consider the statistical inference of the unknown parameter of an exponential distribution based on the time truncated data. The time truncated data occurs quite often in the reliability analysis for type-I or hybrid censoring cases. All the results available today are based on the conditional argument that at least one failure occurs during the experiment. In this paper we provide some inferential results based on the unconditional argument. We extend the results for some two-parameter distributions also.

Interval Estimation of the Unknown Exponential Parameter Based on Time Truncated Data

Abstract: SYNOPTIC ABSTRACTIn this article, we consider the statistical inference of the unknown parameter of an exponential distribution based on the time truncated data. The time truncated data occurs quite often in reliability analysis for type-I or hybrid censoring cases. All results available today are based on the conditional argument that at least one failure occurs during the experiment. In this article, we provide some inferential results based on the unconditional argument. We extend the results for some two-parameter distributions.

On Generalized Progressive Hybrid Censoring in presence of competing risks

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

Inference for Weibull Competing Risks Data Under Generalized Progressive Hybrid Censoring

Abstract: A competing risks model is considered under a generalized progressive hybrid censoring. When the latent failure times are Weibull distributed, maximum-likelihood estimates for the unknown model parameters are established where the associated existence and uniqueness are shown. An asymptotic distribution of the maximum-likelihood estimators is used to construct approximate confidence intervals via the observed fisher information matrix. Moreover, Bayes point estimates and the highest probability density credible intervals of unknown parameters are also presented, and the Gibbs sampling technique is used to approximate corresponding estimates. Simulation studies and real-life example are presented for illustration purpose.

Inference for Weibull competing risks model with partially observed failure causes under generalized progressive hybrid censoring

Abstract: In this paper, a competing risks model is studied when the latent failure times follow Weibull distribution. When the failure times are observed under generalized progressive hybrid censoring and the causes of failure are partially observed, the maximum likelihood estimators of the model parameters are established together with associated existence and uniqueness, and the approximate confidence intervals are constructed based on large sample theory. Bayes estimators and associated credible intervals are obtained under fairly general priors. Moreover, classical and Bayesian inferences are also discussed when there is an order restriction on the scale parameters of the Weibull distributions. Finally, a simulation study and a real data example are presented for illustration.

Multi-sample progressive Type-I censoring of exponentially distributed lifetimes

Abstract: In this paper, we introduce the multi-sample progressive Type-I censoring model where k≥2 independent progressively Type-I censored experiments are conducted. The main objective is the derivation o...

Inference for exponential competing risks data under generalized progressive hybrid censoring

Abstract: In this paper, a competing risks model based on a generalized progressive hybrid censoring is considered. When the latent lifetime distributions of failure causes are exponential distribute...

On Accelerated Life Testing When the AFT Model Fails

Abstract: The accelerated failure time (AFT) model is most commonly used model in accelerated life testing (ALT). This model is restrictive as failure time distributions under different constant stresses differ only in terms of scale. If it is not the case, most papers on ALT use a generalization of the AFT model supposing that under different stresses not only scale but also shape parameters are different. This model has an undesirable property for accelerated experiments—the survival functions corresponding to usual and accelerated stresses intersect. In this paper, we propose flexible generalizations of the AFT model. Estimation procedures and properties of estimators are discussed. Goodness-of-fit (GOF) tests for the given models are proposed. Examples of data analysis are provided. Generalization of the results in case of step stresses is presented.