Ordering Properties of Systems with Two Dependent Components

The study of systems with dependent components from a reliability point of view is a very important topic. However, the majority of the articles study the case of independent components. In this article, we study how the dependency influences the performance of the system. We extend some comparison results obtained in the case of independent components to the case of two dependent components. We show that the more diverse the exponential parameters of the two components, the stronger (weaker) the parallel (series) system in the stochastic ordering. We apply our general results to some common bivariate models in the reliability theory.     

Empirical Likelihood Confidence Region for the Parameter in a Partially Linear Errors-in-Variables Model

In this article, a partially linear errors-in-variables model is considered, and empirical log-likelihood ratio statistic for the unknown parameter in the model is suggested. It is proved that the proposed statistic is asymptotically standard chi-square distribution under some suitable conditions, and hence it can be used to construct the confidence region of the parameter. A simulation study indicates that, in terms of coverage probabilities and average lengths of the confidence intervals, the proposed method performs better than the least-squares method.     

The Asymptotic Estimate of Ruin Probability Under a Class of Risk Model in the Presence of Heavy Tails

In contrast with the classical Cramér–Lundberg model where the premium process is a linear function of time, we consider the ruin probability under the risk model where the aggregate premium consists of both a compound Poisson process and a linear process of time. Moreover, a constant interest force is also taken into account in our model. We restrict ourselves to the case where the claim size is heavy-tailed, i.e., the equilibrium distribution function of the claim size belongs to a wide subclass of the subexponential distribution. An asymptotic formula for the ruin probability is obtained by using the similar method of Kalashnikov and Konstantinides (2000 Kalashnikov , V. , Konstantinides , D. ( 2000 ). Ruin under interest force and subexponential claims: a simple treament . Insur. Math. Econ. 27 : 145 – 149 .[Crossref], [Web of Science ®] , [Google Scholar]). The asymptotic formula we get here is the same as the one in Asmussen (1998 Asmussen , S. ( 1998 ). Subexponential asymptotics for stochastic processes: extremal behaviour, stationary distribution and first passage probabilities . Ann. Appl. Probab. 8 : 354 – 374 .[Crossref], [Web of Science ®] , [Google Scholar]), Klüppelberg and Stadtmüller (1998 Klüppelberg , C. , Stadtmüller , U. ( 1998 ). Ruin probabilities in the presence of heavy-tails and interest rates . Scand. Actuarial J. 1 : 49 – 58 .[Taylor & Francis Online] , [Google Scholar]), and Kalashnikov and Konstantinides (2000 Kalashnikov , V. , Konstantinides , D. ( 2000 ). Ruin under interest force and subexponential claims: a simple treament . Insur. Math. Econ. 27 : 145 – 149 .[Crossref], [Web of Science ®] , [Google Scholar]) which did not consider the stochastic premium.     

A New Formula for Inclusion Probabilities in Median-Ranked Set Sampling

This article develops a new generalized formula to compute the inclusion probabilities of a median-ranked set sample in a finite population setting. The use of this formula is illustrated in a numerical example. Furthermore, the inclusion probabilities of a median-ranked set sample is compared with the inclusion probabilities of ranked set and simple random samples.     

Approximate and Fiducial Confidence Intervals for the Difference Between Two Binomial Proportions

The problem of estimating the difference between two binomial proportions is considered. Closed-form approximate confidence intervals (CIs) and a fiducial CI for the difference between proportions are proposed. The approximate CIs are simple to compute, and they perform better than the classical Wald CI in terms of coverage probabilities and precision. Numerical studies indicate that these approximate CIs can be used safely for practical applications under a simple condition. The fiducial CI is more accurate than the approximate CIs in terms of coverage probabilities. The fiducial CIs, the Newcombe CIs, and the Miettinen–Nurminen CIs are comparable in terms of coverage probabilities and precision. The interval estimation procedures are illustrated using two examples.     

Generalized linear failure rate power series distribution

Abstract

In this article, we introduce a new class of lifetime distributions. This new class includes several previously known distributions such as those of Chahkandi and Ganjali (2009 Chahkandi, M., Ganjali, M. (2009). On some lifetime distributions with decreasing failure rate. Computat. Statist. Data Anal. 53:4433–4440.[Crossref], [Web of Science ®] , [Google Scholar]), Mahmoudi and Jafari (2012 Mahmoudi, E., Jafari, A.A. (2012). Generalized exponential power series distributions. Comput. Statist. Data Anal. 56(12):4047–4066.[Crossref], [Web of Science ®] , [Google Scholar]), and Nadarajah et al. (2012 Nadarajah, S., Shahsanaei, F., Rezaei, S. (2012). A new four-parameter lifetime distribution. J. Statist. Computat. Simul.. ifirst, 1–16. [Google Scholar]). This new class of four-parameter distributions allows for flexible failure rate behavior. Indeed, the failure rate function here can be increasing, decreasing, bathtub-shaped or upside-down bathtub-shaped. Several distributional properties of the new class including moments, quantiles and order statistics are studied. An EM algorithm for computing the estimates of the parameters involved is proposed and some maximum entropy characterizations are discussed. Finally, to show the flexibility and potential of the new class of distributions, applications to two real data sets are provided.     

An application of linear feature selection to estimation of proportions

Let X be a random n-vector whose density function is given by a mixture of known multivariate normal density functions where the corresponding mixture proportions (a priori probabilities) are unknown. We present a numerically tractable method for obtaining estimates of the mixture proportions based on the linear feature selection technique of Guseman, Peters and Walker (1975).     

An emprical bayes approach to two-sample problems with censored data

Empirical Bayes methods are used in estimating the probability based on randomly right-censored samples. The estimator is shown to be asymptotically optimal. Thus, in a way, this uork is similar to the results of Hollander and Korwar (1976) who used a similar approach in estimating A in the case of non-censored data. We also give hero a shorter proof to their rate result. In addition, a. resting procedure is obtained to test the hypothesis against on the basis of censored data. It is shown that this procedure is asymptotically optimal with rate of convergence n . Tnis result is analogous to our earlier result for the uncensored case (1970) The empirical Hayes procedure has been illustrated by means of a practical example.     

A structural model for the markov chain of change in vote intention

Assuming a first-order Markov chain, we propose a structural model for the transition probabilities in vote intention. The proposed model utilizes the ordering among the categories representing vote intentions and carries the flavor of distance models. It also allows a stochastic ordering among distributions reflecting the extent of change. The model is easy to fit and provides a nice interpretation of the data. The model is applied to a panel study of vote intention acquired through six successive interviews before the 1940 Presidential election in Erie County, Ohio.