In this article, we consider the estimation of P[Y < X], when strength, X and stress, Y are two independent variables of Burr Type XII distribution. The MLE of the R based on one simple iterative procedure is obtained. Assuming that the common parameter is known, the maximum likelihood estimator, uniformly minimum variance unbiased estimator and Bayes estimator of P[Y < X] are discussed. The ex...

Competing risks data usually arises in studies in which the death or failure of an individual or an item may be classified into one of T≥2 mutually exclusive causes. In this paper, we will study the competing risks model when the data is progressively first-failure-censored. Based on this type of censoring, we derive the maximum likelihood estimators (MLE's) for the unknown parameters. Approxim...

Stochastic frontier analysis (SFA) is often used to estimate technical efficiency of entities such as firms, countries or municipalities. A potential dependence between the two components of the error term can be taken into account by a copula function. While estimation of the model is straightforward using the Corrected Ordinary Least Squares (COLS) and Maximum Likelihood (ML) methods, an open...

Metrics of phylogenetic tree reliability, such as parametric bootstrap percentages or Bayesian posterior probabilities, represent internal measures of the topological reproducibility of a phylogenetic tree, while the recently introduced aLRT (approximate likelihood ratio test) assesses the likelihood that a branch exists on a maximum-likelihood tree. Although those values are often equated with...

For a continuous-scale diagnostic test, the most commonly used summary index of the receiver operating characteristic curve (ROC) is the area under the curve (AUC) that measures the accuracy of the diagnostic test. In this article, we propose an empirical likelihood (EL) approach for the inference on the AUC. First we define an EL ratio for the AUC and show that its limiting distribution is a s...

In this paper, we develop statistical inference of competing risks samples which are collected under a joint Type-II censoring scheme products with Weibull lifetime distributions. These inferences drawn from two independent fatal and come different lines production the same facility. The model parameters life (reliability hazard rate functions) estimated using maximum likelihood (ML), bootstrap...

The authors examine the robustness of empirical likelihood ratio (ELR) confidence intervals for the mean and M -estimate of location. They show that the ELR interval for the mean has an asymptotic breakdown point of zero. They also give a formula for computing the breakdown point of the ELR interval for M -estimate. Through a numerical study, they further examine the relative advantages of the ...