Statistical Inference of Left Truncated and Right Censored Data from Marshall–Olkin Bivariate Rayleigh Distribution

Abstract

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.

Likelihood Inference for Copula Models Based on Left-Truncated and Competing Risks Data from Field Studies

“…In this paper, we propose a copula-based model for dependent competing risks in the presence of left-truncation. The copula-based competing risks model permits more flexible failure time distributions and dependence structure than the existing competing risks model [4,26,27]. Parametric likelihood-based inference methods are then formulated, motivated by the practically important applications in field reliability analyses.…”

“…Existing competing risks analyses for left-truncated field data are limited to the following models: the independent Weibull model with the common shape parameter [26], the Marshall-Olkin bivariate Rayleigh model [27], and the Marshall-Olkin bivariate Weibull model [4]. While these three models provide an important starting point, their models are somewhat specific for modeling latent failure times of competing risks.…”

“…In this paper, we will develop copula-based models for dependent competing risks under left-truncation, permitting more flexible models for dependence structure and failure time distributions than the existing three models of [4,26,27]. Due to our main interest in applications to reliability analyses, we adopt the standard parametric distributions, including the Weibull, lognormal, and gamma distributions.…”

Inference on the Beta Type I Generalized Half Logistic Distribution Under Right Censored Observation with Application to Covid-19

“…It was revealed from the result that the estimates performed well due to reducing values of average estimates coupling with the mean square error as the sample sizes increase. We further applied this model to COVID-19 data [8,18,21,22].…”

Left‐truncated and right‐censored field failure data: Review of parametric analysis for reliability

“…16 Therefore, the paper adds these recent developments to the previous review of Balakrishnan and Mitra. 14 The paper also discusses potential future works on this growing research area, including the emerging methods for interval censoring 6,25 and competing risks 26,27 for field failure data. Our focus is on the parametric methods that can be applicable for reliability engineering based on field failure data.…”