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This article provides a simple expression of the Fisher information matrix about the unknown parameter(s) of the underlying lifetime model under the generalized progressive hybrid censoring scheme. The expressions of the expected number of failures and the expected duration of life test are also derived. Exponential and Weibull lifetime models are considered for numerical illustrations. Finally, Fisher information-based optimal schemes are discussed for the Weibull lifetime model. [ABSTRACT FROM AUTHOR]

Reduced-rank regression is a dimensionality reduction method with many applications. The asymptotic theory for reduced rank estimators of parameter matrices in multivariate linear models has been studied extensively. In contrast, few theoretical results are available for reduced-rank multivariate generalized linear models. We develop M-estimation theory for concave criterion functions that are maximized over parameter spaces that are neither convex nor closed. These results are used to derive the consistency and asymptotic distribution of maximum likelihood estimators in reduced-rank multivariate generalized linear models, when the response and predictor vectors have a joint distribution. We illustrate our results in a real data classification problem with binary covariates. [ABSTRACT FROM AUTHOR]

In the present paper, we establish the moderate deviations principle for the maximum-likelihood estimator (MLE) from independent not identically sample under some suitable assumptions, which are weaker than the exponential integrability condition in Miao and Chen [Note on the moderate deviation principle of maximum likelihood estimator. Acta Appl Math. 2010;110:863–869] and give an equivalent condition of the moderate deviations principle for the MLE under the i.i.d. case. [ABSTRACT FROM PUBLISHER]

The family of skew distributions introduced by Azzalini and extended by others has received widespread attention. However, it suffers from complicated inference procedures. In this paper, a new family of skew distributions that overcomes the difficulties is introduced. This new family belongs to the exponential family. Many properties of this family are studied, inference procedures developed and simulation studies performed to assess the procedures. Some particular cases of this family, evidence of its flexibility and a real data application are presented. At least 10 advantages of the new family over Azzalini's distributions are established. [ABSTRACT FROM PUBLISHER]

Frailty models are often used to describe the extra heterogeneity in survival data by introducing an individual random, unobserved effect. The frailty term is usually assumed to act multiplicatively on a baseline hazard function common to all individuals. In order to apply the frailty model, a specific frailty distribution has to be assumed. If at least one of the latent variables is continuous, the frailty must follow a continuous distribution. In this paper, a finite mixture of continuous frailty distributions is used in order to describe situations in which one (or more) of the latent variables separates the population in study into two (or more) subpopulations. Closure properties of the unobserved quantity are given along with the maximum-likelihood estimates under the most common choices of frailty distributions. The model is illustrated on a set of lifetime data. [ABSTRACT FROM AUTHOR]

Epstein [Truncated life tests in the exponential case, Ann. Math. Statist. 25 (1954), pp. 555–564] introduced a hybrid censoring scheme (called Type-I hybrid censoring) and Chen and Bhattacharyya [Exact confidence bounds for an exponential parameter under hybrid censoring, Comm. Statist. Theory Methods 17 (1988), pp. 1857–1870] derived the exact distribution of the maximum-likelihood estimator (MLE) of the mean of a scaled exponential distribution based on a Type-I hybrid censored sample. Childs et al. [Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution, Ann. Inst. Statist. Math. 55 (2003), pp. 319–330] provided an alternate simpler expression for this distribution, and also developed analogous results for another hybrid censoring scheme (called Type-II hybrid censoring). The purpose of this paper is to derive the exact bivariate distribution of the MLE of the parameter vector of a two-parameter exponential model based on hybrid censored samples. The marginal distributions are derived and exact confidence bounds for the parameters are obtained. The results are also used to derive the exact distribution of the MLE of the pth quantile, as well as the corresponding confidence bounds. These exact confidence intervals are then compared with parametric bootstrap confidence intervals in terms of coverage probabilities. Finally, we present some numerical examples to illustrate the methods of inference developed here. [ABSTRACT FROM PUBLISHER]

Generalized order statistics, and thus sequential order statistics with conditional proportional hazard rates, are shown to form a regular exponential family in the model parameters. This structure is utilized to derive maximum likelihood estimators for these parameters or functions of them along with several properties of the estimators. The Fisher information matrix is stated, and asymptotic efficiency is shown. [ABSTRACT FROM PUBLISHER]

A problem of Bayesian sequential estimating an unknown parameter of a time-transformed exponential model is considered. It is supposed that the loss associated with the error of estimation is weighted squared or precautionary and the cost of observing the process is a function of time and the number of observations. Bayes sequential procedures for estimating the unknown parameter are presented. [ABSTRACT FROM AUTHOR]

The hybrid censoring scheme, which is a mixture of Type-I and Type-II censoring schemes, has been extended to the case of progressive censoring schemes by Kundu and Joarder [Analysis of Type-II progressively hybrid censored data, Comput. Stat. Data Anal. 50 (2006), pp. 2509–2528] and Childs et al. [Exact likelihood inference for an exponential parameter under progressive hybrid censoring schemes, in Statistical Models and Methods for Biomedical and Technical Systems, F. Vonta, M. Nikulin, N. Limnios, and C. Huber-Carol, eds., Birkhäuser, Boston, MA, 2007, pp. 323–334]. In this paper, we derive a simple expression for the Fisher information contained in Type-I and Type-II progressively hybrid censored data. An illustrative example is provided applicable to a scaled-exponential distribution to demonstrate our methodologies. [ABSTRACT FROM PUBLISHER]

In this paper, we study ordering properties of lifetimes of parallel systems with two independent heterogeneous exponential components in terms of the likelihood ratio order (reversed hazard rate order) and the hazard rate order (stochastic order). We establish, among others, that the weakly majorization order between two hazard rate vectors is equivalent to the likelihood ratio order (reversed hazard rate order) between lifetimes of two parallel systems, and that the p-larger order between two hazard rate vectors is equivalent to the hazard rate order (stochastic order) between lifetimes of two parallel systems. Moreover, we extend the results to the proportional hazard rate models. The results derived here strengthen and generalize some of the results known in the literature. [ABSTRACT FROM PUBLISHER]

A generalization of the exponential distribution is presented. The generalization always has its mode at zero and yet allows for increasing, decreasing and constant hazard rates. It can be used as an alternative to the gamma, Weibull and exponentiated exponential distributions. A comprehensive account of the mathematical properties of the generalization is presented. A real data example is discussed to illustrate its applicability. [ABSTRACT FROM PUBLISHER]

Wei et al. [B.C. Wei, J.Q. Shi, W.K. Fung, and Y.Q. Hu, Testing for varying dispersion in exponential family nonlinear models, Ann. Inst. Statist. Math. 50 (1998), pp. 277-294.] developed the score diagnostics for varying dispersion in exponential family nonlinear models, such as the normal, inverse Gaussian, and gamma models, and investigated the powers of these tests through Monte Carlo simulations. In this paper, the asymptotic behaviours, including asymptotic chi-square and approximate powers under local alternatives of the score tests, are studied and examined by Monte Carlo simulations. The methods to estimate local powers of the score tests are illustrated with Grass yield data [P. McCullagh, and J.A. Nelder, Generalized Linear Models, Chapman and Hall, London (1989).]. [ABSTRACT FROM AUTHOR]

In this paper, we examine the relationships between log odds rate and various reliability measures such as hazard rate and reversed hazard rate in the context of repairable systems. We also prove characterization theorems for some families of distributions viz. Burr, Pearson and log exponential models. We discuss the properties and applications of log odds rate in weighted models. Further we extend the concept to the bivariate set up and study its properties. [ABSTRACT FROM AUTHOR]

We obtain the possible limit distributions of unbiased estimators of functions of the parameter of a natural exponential family. The limit distribution depends on j, the order of the first non-zero derivative at the true (but usually unknown) value of the parameter. We show that if j ≥2 then the umvu and the maximum likelihood estimators are not asymptotically equivalent. [ABSTRACT FROM AUTHOR]

Let {\bf X} be a random vector in R^{n} with probability density f({\bf x}) = c_{n} \exp \{-({\bf x}\prime {\bf x})^{n/2}\} . We show that the random variable U = f({\bf X}) has uniform distribution on (0, c_{n}) . Our result generalizes previously derived special cases n = 1 (the Laplace distribution) and n = 2 (the uncorrelated bivariate normal distribution). [ABSTRACT FROM AUTHOR]