Statistical Inference in Dependent Component Hybrid Systems with Masked Data

Complex systems are usually composed of simple hybrid systems. In this paper, we consider statistical inference for two fundamental hybrid systems: series-parallel and parallel-series systems based on masked data. Assuming dependent lifetimes of components modelled by Marshall and Olkin’s bivariate exponential distribution in the system, we present maximum likelihood and interval estimation of parameters of interest. Intensive simulation studies are performed to demonstrate the efficiency of the methods.

Estimation of the Derivatives of a Function in a Convolution Regression Model with Random Design

A convolution regression model with random design is considered. We investigate the estimation of the derivatives of an unknown function, element of the convolution product. We introduce new estimators based on wavelet methods and provide theoretical guarantees on their good performances.

Estimation in Step-Stress Accelerated Life Tests for Power Generalized Weibull Distribution with Progressive Censoring

Based on progressive censoring, step-stress partially accelerated life tests are considered when the lifetime of a product follows power generalized Weibull distribution. The maximum likelihood estimates (MLEs) and Bayes estimates (BEs) are obtained for the distribution parameters and the acceleration factor. In addition, the approximate and bootstrap confidence intervals (CIs) of the estimators are presented. Furthermore, the optimal stress change time for the step-stress partially accelerated life test is determined by minimizing the asymptotic variance of MLEs of the model parameters and the acceleration factor. Simulation results are carried out to study the precision of the MLEs and BEs for the parameters involved.

Bayesian Estimation of Inequality and Poverty Indices in Case of Pareto Distribution Using Different Priors under LINEX Loss Function

Bayesian estimators of Gini index and a Poverty measure are obtained in case of Pareto distribution under censored and complete setup. The said estimators are obtained using two noninformative priors, namely, uniform prior and Jeffreys’ prior, and one conjugate prior under the assumption of Linear Exponential (LINEX) loss function. Using simulation techniques, the relative efficiency of proposed estimators using different priors and loss functions is obtained. The performances of the proposed estimators have been compared on the basis of their simulated risks obtained under LINEX loss function.

Relative Entropies and Jensen Divergences in the Classical Limit

Metrics and distances in probability spaces have shown to be useful tools for physical purposes. Here we use this idea, with emphasis on Jensen Divergences and relative entropies, to investigate features of the road towards the classical limit. A well-known semiclassical model is used and recourse is made to numerical techniques, via the well-known Bandt and Pompe methodology, to extract probability distributions from the pertinent time-series associated with dynamical data.

Generalized Estimating Equations in Longitudinal Data Analysis: A Review and Recent Developments

Generalized Estimating Equation (GEE) is a marginal model popularly applied for longitudinal/clustered data analysis in clinical trials or biomedical studies. We provide a systematic review on GEE including basic concepts as well as several recent developments due to practical challenges in real applications. The topics including the selection of “working” correlation structure, sample size and power calculation, and the issue of informative cluster size are covered because these aspects play important roles in GEE utilization and its statistical inference. A brief summary and discussion of potential research interests regarding GEE are provided in the end.

On Marginal Dependencies of the 2 × 2 Kappa

Cohen’s kappa is a standard tool for the analysis of agreement in a 2 × 2 reliability study. Researchers are frequently only interested in the kappa-value of a sample. Various authors have observed that if two pairs of raters have the same amount of observed agreement, the pair whose marginal distributions are more similar to each other may have a lower kappa-value than the pair with more divergent marginal distributions. Here we present exact formulations of some of these properties. The results provide a better understanding of the 2 × 2 kappa for situations where it is used as a sample statistic.

Designing Bayesian Sampling Plans with Adaptive Progressive Hybrid Censored Samples

This paper studies the acceptance sampling for exponential distributions with type-I and type-II adaptive progressive hybrid censored samples. Algorithms are proposed for deriving Bayesian sampling plans. We compare the performance of the proposed sampling plans with the sampling plans of Lin and Huang (2012). The numerical results indicate that the proposed sampling plans outperform the sampling plans of Lin and Huang (2012).

Statistical Analysis of a Weibull Extension with Bathtub-Shaped Failure Rate Function

We consider the parameter inference for a two-parameter life distribution with bathtub-shaped or increasing failure rate function. We present the point and interval estimations for the parameter of interest based on type-II censored samples. Through intensive Monte-Carlo simulations, we assess the performance of the proposed estimation methods by a comparison of precision. Example applications are demonstrated for the efficiency of the methods.

Statistical Test for Bivariate Uniformity

The purpose of the multidimension uniformity test is to check whether the underlying probability distribution of a multidimensional population differs from the multidimensional uniform distribution. The multidimensional uniformity test has applications in various fields such as biology, astronomy, and computer science. Such a test, however, has received less attention in the literature compared with the univariate case. A new test statistic for checking multidimensional uniformity is proposed in this paper. Some important properties of the proposed test statistic are discussed. As a special case, the bivariate statistic test is discussed in detail in this paper. The Monte Carlo simulation is used to compare the power of the newly proposed test with the distance-to-boundary test, which is a recently published statistical test for multidimensional uniformity. It has been shown that the test proposed in this paper is more powerful than the distance-to-boundary test in some cases.