Likelihood Ratio Order of m-Spacings in Multiple-Outlier Models

This article deals with the multiple-outlier exponential model. The likelihood ratio order between m-spacings of the combined sample is developed, some results extend the conclusions on simple spacings in Wen et al. (2007 Wen , S. , Lu , Q. , Hu , T. ( 2007 ). Likelihood ratio order of spacings of heterogeneous exponential random variables . J. Multivariate Anal. 98 : 743 – 756 .[Crossref], [Web of Science ®] , [Google Scholar]).     

Are the Order Statistics Ordered? A Survey of Recent Results

The distributions of coherent systems with components with exchangeable lifetimes can be represented as mixtures of distributions of order statistics (k-out-of-n systems) from possibly dependent samples by using the concept of the signature of Samaniego (1985 Samaniego , F. ( 1985 ). On closure of the IFR class under formation of coherent systems . IEEE Trans. Reliabil. R-34 : 69 – 72 .[Crossref], [Web of Science ®] , [Google Scholar]). This representation, together with Rychlik's (1993 Rychlik , T. ( 1993 ). Bounds for expectation of L-estimates for dependent samples . Statistics 24 : 1 – 7 .[Taylor & Francis Online] , [Google Scholar]) results, can be used to obtain sharp bounds on the distribution (or the reliability) function and on the expected lifetime of the system. Also, this representation can be used to determine the asymptotic behavior of the hazard rate of the system when the order statistics are ordered in the hazard rate order. Moreover, the lifetime distributions of coherent systems (and in particular, of order statistics) can also be represented as generalized mixtures (that is, mixtures with some negative weights) of distributions of series system lifetimes by using the concept of the minimal signature defined by Navarro et al. (2007a Navarro , J. , Ruiz , J. M. , Sandoval , C. J. ( 2007a ). Properties of coherent systems with dependent components . Commun. Statist. Theory Methods 36 : 175 – 191 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). This representation can also be used to determine the final behavior of the hazard rate of the system through the behavior of the hazard rate of the series systems. In particular, it can be used to show that the order statistics are, under some conditions, asymptotically hazard rate ordered. However, in general, this result is not true, that is, the order statistics need not be hazard rate ordered.     

Marshall–Olkin Extended Lomax Distribution and Its Application to Censored Data

The problem of making statistical inference about θ =P(X > Y) has been under great investigation in the literature using simple random sampling (SRS) data. This problem arises naturally in the area of reliability for a system with strength X and stress Y. In this study, we will consider making statistical inference about θ using ranked set sampling (RSS) data. Several estimators are proposed to estimate θ using RSS. The properties of these estimators are investigated and compared with known estimators based on simple random sample (SRS) data. The proposed estimators based on RSS dominate those based on SRS. A motivated example using real data set is given to illustrate the computation of the newly suggested estimators.     

Multiple Comparison Procedures: The Practical Solution

A practicing statistician looks at the multiple comparison controversy and related issues through the eyes of the users. The concept of consistency is introduced and discussed in relation to five of the more common multiple comparison procedures. All of the procedures are found to be inconsistent except the simplest procedure, the unrestricted least significant difference (LSD) procedure (or multiple t test). For this and other reasons the unrestricted LSD procedure is recommended for general use, with the proviso that it should be viewed as a hypothesis generator rather than as a method for simultaneous hypothesis generation and testing. The implications for Scheffé's test for general contrasts are also discussed, and a new recommendation is made.     

A Bayes comparison of Weibull extension and modified Weibull models for data showing bathtub hazard rate

A number of models have been proposed in the literature to model data reflecting bathtub-shaped hazard rate functions. Mixture distributions provide the obvious choice for modelling such data sets but these contain too many parameters and hamper the accuracy of the inferential procedures particularly when the data are meagre. Recently, a few distributions have been proposed which are simply generalizations of the two-parameter Weibull model and are capable of producing bathtub behaviour of the hazard rate function. The Weibull extension and the modified Weibull models are two such families. This study focuses on comparing these two distributions for data sets exhibiting bathtub shape of the hazard rate. Bayesian tools are preferred due to their wide range of applicability in various nested and non-nested model comparison problems. Real data illustrations are provided so that a particular model can be recommended based on various tools of model comparison discussed in the paper.     

Income vulnerability of rural households in Bangladesh: a comparison between Bayesian and classical methods

The geographical location and the monsoon climate render Bangladesh highly vulnerable to natural hazards, deteriorating the country's socio-economic stability. This study is based on 500 randomly chosen rural households from the Household Income and Expenditure Survey [Bangladesh Bureau of Statistics, Planning Division, Ministry of Planning, Government of the People's Republic of Bangladesh, Dhaka, 2006]. The objectives are to estimate the income vulnerability of rural households and to check whether the Bayesian approaches (natural conjugate prior and non-informative prior estimates) have any superiority over the classical (feasible generalized least square (FGLS)) method. The poverty level, measured from the data, is 24%; whereas the vulnerability estimates, using FGLS, natural conjugate prior and non-informative prior are 31%, 69% and 82%, respectively. Vulnerability estimates by the Bayesian natural conjugate prior approach is found to have greater efficiency compared with FGLS and non-informative prior approaches.     

Reducing component estimation for varying coefficient models

The estimation problem for varying coefficient models has been studied by many authors. We consider the problem in the case that the unknown functions admit different degrees of smoothness. In this paper we propose a reducing component local polynomial method to estimate the unknown functions. It is shown that all of our estimators achieve the optimal convergence rates. The asymptotic distributions of our estimators are also derived. The established asymptotic results and the simulation results show that our estimators outperform the the existing two-step estimators when the coefficient functions admit different degrees of smoothness. We also develop methods to speed up the estimation of the model and the selection of the bandwidths.     

Some results on the mean residual waiting time of records

Often, in reliability theory, risk analysis, renewal processes and actuarial studies, mean residual life function or life expectancy plays an important role in studying the conditional tail measure of lifetime data. In this paper, we introduce the notion of the mean residual waiting time of records and present some monotonic and aging properties. Sharp bounds for the mean residual waiting time of records are also investigated.     

Some characterization results for parallel systems with two heterogeneous exponential components

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.     

Bayesian factor models in characterizing molecular adaptation

Assessing the selective influence of amino acid properties is important in understanding evolution at the molecular level. A collection of methods and models has been developed in recent years to determine if amino acid sites in a given DNA sequence alignment display substitutions that are altering or conserving a prespecified set of amino acid properties. Residues showing an elevated number of substitutions that favorably alter a physicochemical property are considered targets of positive natural selection. Such approaches usually perform independent analyses for each amino acid property under consideration, without taking into account the fact that some of the properties may be highly correlated. We propose a Bayesian hierarchical regression model with latent factor structure that allows us to determine which sites display substitutions that conserve or radically change a set of amino acid properties, while accounting for the correlation structure that may be present across such properties. We illustrate our approach by analyzing simulated data sets and an alignment of lysin sperm DNA.