Reliability of stress–strength model for exponentiated Pareto distributions

In this paper, the reliability of a system is discussed when the strength of the system and the stress imposed on it are independent, non-identical exponentiated Pareto distributed random variables. Different point estimations and interval estimations are proposed. The point estimators obtained are maximum likelihood, uniformly minimum variance unbiased and Bayesian estimators. The interval estimations obtained are approximate, exact, bootstrap-p and bootstrap-t confidence intervals and Bayesian credible interval. Different methods and the corresponding confidence intervals are compared using Monte-carlo simulations.     

The labour market flexibility debate in India: Re‐examining the case for signing voluntary contracts

A major focus of India's ongoing policy debate over labour market flexibilization has been the statutory requirement that firms employing 100 or more workers cannot dismiss employees without prior government permission. The case for repealing that requirement (or greatly increasing the workforce threshold) is notably underpinned by Basu, Fields and Debgupta (2009). Here, the author challenges their particular theoretical argument for hiring and firing at will based on the voluntary signing of contracts, demonstrating that their general policy conclusion is logically unsustainable even within the framework of that model. The case for labour market flexibilization through voluntary contracting thus remains unfounded.     

A new approach to statistical efficiency of weighted least squares fitting algorithms for reparameterization of nonlinear regression models

We study nonlinear least-squares problem that can be transformed to linear problem by change of variables. We derive a general formula for the statistically optimal weights and prove that the resulting linear regression gives an optimal estimate (which satisfies an analogue of the Rao-Cramer lower bound) in the limit of small noise.     

Prediction intervals for future Weibull residual data

In reliability theory, risk analysis, renewal processes and actuarial studies, the residual lifetimes data play an important essential role in studying the conditional tail of the lifetime data. In this paper, based on some observed ordered residual Weibull data, we introduce different prediction methods for obtaining prediction intervals (PIs) of future residual lifetimes including likelihood, Wald, moments, parametric bootstrap, and highest conditional methods. Monte Carlo simulations are performed to compare the performances of the so obtained PIs and one data analysis is performed for illustration purposes.     

A new generalization of alpha-skew-normal distribution

In this paper, a new generalization of alpha-skew-normal distribution is considered. Some properties of this distribution, which is denoted by GASN(α, λ), including moments, maximum likelihood estimation of parameters, and some other properties are studied. Finally, using a real data set, we show that our new distribution is the best-fitted distribution for the used data among normal, skew normal, alpha-skew-normal, and skew-bimodal-normal distributions.     

Local composite quantile regression estimation of time-varying parameter vector for multidimensional time-inhomogeneous diffusion models

This paper is dedicated to the study of the composite quantile regression (CQR) estimations of time-varying parameter vectors for multidimensional diffusion models. Based on the local linear fitting for parameter vectors, we propose the local linear CQR estimations of the drift parameter vectors, and verify their asymptotic biases, asymptotic variances and asymptotic normality. Moreover, we discuss the asymptotic relative efficiency (ARE) of the local linear CQR estimations with respect to the local linear least-squares estimations. We obtain that the local estimations that we proposed are much more efficient than the local linear least-squares estimations. Simulation studies are constructed to show the performance of the estimations proposed.     

Accelerated life test sampling plans for the Weibull distribution under Type I progressive interval censoring with random removals

This paper considers the design of accelerated life test (ALT) sampling plans under Type I progressive interval censoring with random removals. We assume that the lifetime of products follows a Weibull distribution. Two levels of constant stress higher than the use condition are used. The sample size and the acceptability constant that satisfy given levels of producer's risk and consumer's risk are found. In particular, the optimal stress level and the allocation proportion are obtained by minimizing the generalized asymptotic variance of the maximum likelihood estimators of the model parameters. Furthermore, for validation purposes, a Monte Carlo simulation is conducted to assess the true probability of acceptance for the derived sampling plans.     

The empirical Bayes estimators of the parameter of the Poisson distribution with a conjugate gamma prior under Stein's loss function

For the hierarchical Poisson and gamma model, we calculate the Bayes posterior estimator of the parameter of the Poisson distribution under Stein's loss function which penalizes gross overestimation and gross underestimation equally and the corresponding Posterior Expected Stein's Loss (PESL). We also obtain the Bayes posterior estimator of the parameter under the squared error loss and the corresponding PESL. Moreover, we obtain the empirical Bayes estimators of the parameter of the Poisson distribution with a conjugate gamma prior by two methods. In numerical simulations, we have illustrated: The two inequalities of the Bayes posterior estimators and the PESLs; the moment estimators and the Maximum Likelihood Estimators (MLEs) are consistent estimators of the hyperparameters; the goodness-of-fit of the model to the simulated data. The numerical results indicate that the MLEs are better than the moment estimators when estimating the hyperparameters. Finally, we exploit the attendance data on 314 high school juniors from two urban high schools to illustrate our theoretical studies.     

An Extended Single‐index Model with Missing Response at Random

An extended single‐index model is considered when responses are missing at random. A three‐step estimation procedure is developed to define an estimator for the single‐index parameter vector by a joint estimating equation. The proposed estimator is shown to be asymptotically normal. An algorithm for computing this estimator is proposed. This algorithm only involves one‐dimensional nonparametric smoothers, thereby avoiding the data sparsity problem caused by high model dimensionality. Some simulation studies are conducted to investigate the finite sample performances of the proposed estimators.