A stochastic restricted k–d class estimator

In this paper, we introduce a stochastic restricted k–d class estimator for the vector of parameters in a linear model when additional linear restrictions on the parameter vector are assumed to hold. The stochastic restricted k–d class estimator is a generalization of the ordinary mixed estimator and the k–d class estimator. We show that our new biased estimator is superior in the mean squared error matrix sense to the k–d class estimator [S. Sakall?o?lu and S. Kaçiranlar, A new biased estimator based on ridge estimation, Statist. Papers 49 (2008), pp. 669–689] and the stochastic restricted Liu estimator [H. Yang and J.W. Xu, An alternative stochastic restricted Liu estimator in linear regression, Statist. Papers 50 (2009), pp. 639–647]. Finally, a numerical example is given to show the theoretical results.     

The beta-Weibull geometric distribution

We propose a new distribution, the so-called beta-Weibull geometric distribution, whose failure rate function can be decreasing, increasing or an upside-down bathtub. This distribution contains special sub-models the exponential geometric [K. Adamidis and S. Loukas, A lifetime distribution with decreasing failure rate, Statist. Probab. Lett. 39 (1998), pp. 35–42], beta exponential [S. Nadarajah and S. Kotz, The exponentiated type distributions, Acta Appl. Math. 92 (2006), pp. 97–111; The beta exponential distribution, Reliab. Eng. Syst. Saf. 91 (2006), pp. 689–697], Weibull geometric [W. Barreto-Souza, A.L. de Morais, and G.M. Cordeiro, The Weibull-geometric distribution, J. Stat. Comput. Simul. 81 (2011), pp. 645–657], generalized exponential geometric [R.B. Silva, W. Barreto-Souza, and G.M. Cordeiro, A new distribution with decreasing, increasing and upside-down bathtub failure rate, Comput. Statist. Data Anal. 54 (2010), pp. 935–944; G.O. Silva, E.M.M. Ortega, and G.M. Cordeiro, The beta modified Weibull distribution, Lifetime Data Anal. 16 (2010), pp. 409–430] and beta Weibull [S. Nadarajah, G.M. Cordeiro, and E.M.M. Ortega, General results for the Kumaraswamy-G distribution, J. Stat. Comput. Simul. (2011). DOI: 10.1080/00949655.2011.562504] distributions, among others. The density function can be expressed as a mixture of Weibull density functions. We derive expansions for the moments, generating function, mean deviations and Rénvy entropy. The parameters of the proposed model are estimated by maximum likelihood. The model fitting using envelops was conducted. The proposed distribution gives a good fit to the ozone level data in New York.     

On the Distribution of Matrix Quadratic Forms

A characterization of the distribution of the multivariate quadratic form given by X A X′, where X is a p × n normally distributed matrix and A is an n × n symmetric real matrix, is presented. We show that the distribution of the quadratic form is the same as the distribution of a weighted sum of non central Wishart distributed matrices. This is applied to derive the distribution of the sample covariance between the rows of X when the expectation is the same for every column and is estimated with the regular mean.     

Nested Latin Hypercube Designs with Sliced Structures

In computer experiments, space-filling designs with a sliced structure or nested structure have received much recent interest and been studied separately. However, it is likely that designs with both structures are needed in some situations, but there are no suitable designs so far. In this paper, we construct a special class of nested Latin hypercube designs with sliced structures, in such a design, a small sliced Latin hypercube design is nested within a large one. The construction method is easy to implement and the number of factors is flexible. Numerical simulations show the usefulness of the newly proposed designs.     

Bayesian Inferences and Forecasts With Multiple Autoregressive Moving Average Models

The main objective of this paper is to develop convenient Bayesian techniques for estimation and forecasting which can be used to analyze multiple (multivariate) autoregressive moving average processes. Based on the conditional likelihood function and the least squares estimates of the residuals, the marginal posterior distribution of the coefficients of the model is approximated by a matrix t distribution, the marginal posterior distribution of the precision matrix is approximated by a Wishart distribution, and the predictive distribution is approximated by a multivariate t distribution. Some numerical examples are given to demonstrate the idea of using the proposed techniques to analyze different types of multiple ARMA models.     

Some Improvements in Numerical Evaluation of Symmetric Stable Density and Its Derivatives

A new multivariate inverse Polya distribution of order k, type I, is derived by means of a generalized urn scheme and by compounding the multivariate negative binomial distribution of order k, type I, of Philippou, Antzoulakos and Tripsiannis (1988) with the Dirichlet distribution. It is noted that this new distribution includes as special cases a new multivariate inverse hypergeometric distribution of order k and a new multivariate negative inverse one of the same order. The mean and variance-covariance of the multivariate inverse Polya distribution of order k, type I, are derived, and two known distributions of the same order are shown to be limiting cases of it.     

Confidence Intervals for the Scale Parameter of the Power-Law Process

The power-law process (PLP) is a two-parameter model widely used for modeling repairable system reliability. Results on exact point estimation for both parameters as well as exact interval estimation for the shape parameter are well known. In this paper, we investigate the interval estimation for the scale parameter. Asymptotic confidence intervals are derived using Fisher information matrix and theoretical results by Cocozza-Thivent (1997 Cocozza-Thivent , C. ( 1997 ). Processus Stochastiques et Fiabilité des Systèmes . Berlin : Springer-Verlag . [Google Scholar]). The accuracy of the interval estimation for finite samples is studied by simulation methods.     

An algorithm for the estimation of poisson regressions involving structural change

We consider the estimation of Poisson regression models in which structural variation in a subset of the parameters is permitted. It is noted that coventional estimation algorithms are likely to impose restrictions on the number of explanatory variables and the number of structural regimes. We propose an alternative algorithm that implements partitioned matrix inversion and thereby avoids restictions on the size of the model. The algorithm is applied to a model of shopping behavior Adjustments in the algorithm necessary for dealing with censored data are detailed.     

Performance analysis of machine repair system with single working vacation

Abstract

This paper studies a machine repair problem with repairman’s single working vacation in which repairman works with a lower repair rate rather than completely terminating repair during vacation period. Employing Markov process theory and matrix analytical method, various system performance measures are obtained in transient and stationary regimes. Moreover, we deduce the system reliability, the mean time to failure, the repairman’s busy period and the waiting time of failed machine by using the probabilistic properties of phase type distribution. Further, some numerical examples are provided. Finally, a cost model is developed to determine the optimum value of operating machines.