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This paper establishes the asymptotic behaviour for the covariance matrix and the limit distributions of the least squares estimators for a regression coefficients in a multivariate continuous regression models with long-memory Gaussian errors. The used method is based on the asymptotic analysis of orthogonal expansion of non-linear functionals of homogeneous and isotropic Gaussian random fields. [Copyright &y& Elsevier]

In this paper, we focus on a multivariate continuous regression model with long-memory stationary Gaussian errors. Some upper bounds on the rate of convergence in the Central Limit Theorem for normalized least square estimators (LSE) in these regression models are obtained. The used method is based on the asymptotic analysis of orthogonal expansion of non linear functionals of stationary Gaussian processes and on the Kolmogorov distance. [Copyright &y& Elsevier]

In the spirit of [J. Statist. Planning Inf. 92 (2001) 121], a moment inequality for the class of new better than used failure rate NBUFR (NWUFR) of aging distributions is derived. From this inequality we constructed a new family of test statistics. We used this family in testing exponentiality against NBUFR (NWUFR). The asymptotic normality of the proposed statistic is presented. Pitman asymptotic efficacy, the power and critical values of the proposed statistic are calculated. It is shown that, the proposed statistic has a high asymptotic relative efficiency with respect to tests of other classes for commonly used alternatives. [Copyright &y& Elsevier]

In a recent paper, Ahmad [J. Statist. Plann. Inference 92 (2001) 121] proposes a family of tests for new better than used, new better than used in expectation and harmonic new better than used in expectation. His family of tests is based on some moment inequalities of these classes. In this paper we present a family of tests to test exponentiality against increasing failure rate average (IFRA) alternatives. Our proposed family is based on a moment inequality of the IFRA class. The results of a Pitman asymptotic relatives efficiency comparison indicate the superiority of our tests. [Copyright &y& Elsevier]

The random residual lifetime is a random variable representing the remaining life of a system of age x⩾0. The mean residual life at age x, is the expected value of the remaining life beyond that age which is well known and extensively studied for both testing and estimation.In this article, a new approach is presented for testing constant versus decreasing residual life. The new test is much simpler to compute, asymptotically normal and performs better than previous tests in terms of power and Pitman asymptotic efficiencies for several alternatives. [Copyright &y& Elsevier]

In this paper we estimate the reliability of the individual components that belong to a parallel system using masked-system life test data. In particular, we compute the maximum likelihood and Bayes estimates of component reliabilities. The considered system consists of J independent components having non-identical complementary exponential lifetime distributions. It is assumed for Bayes estimates that the unknown parameters are independent random variables having symmetrical triangle probability density functions. The approaches are illustrated with a two-component parallel system. A numerical simulation study is introduced to show how one can use the present approaches to compute these estimations for a practical problem. Also in the numerical simulation study a comparison between Bayes and maximum likelihood estimates is introduced. [Copyright &y& Elsevier]