Stochastic comparisons of two-unit repairable systems

Abstract

We consider two models of two-unit repairable systems: cold standby system and warm standby system. We suppose that the lifetimes and repair times of the units are all independent exponentially distributed random variables. Using stochastic orders we compare the lifetimes of systems under different assumptions on the parameters of exponential distributions. We also consider a cold standby system where the lifetimes and repair times of its units are not necessarily exponentially distributed.     

Goodness of fit for the poisson distribution based on the probability generating function

For testing the fit of a discrete distribution, use of the probability generating function and its empirical counterpart has been suggested in Koeherlakota and Kocherlakota (1986). In the present paper, a particular functional of the corresponding empirical probability generating function process is proposed as a measure to test the discrepancy between the evidence and the hypothesis. The asymptotic behavior of the empirical probability generating function when a parameter is estimated is obtained, The study is exemplified for the Poisson case only but the procedure can be extended to other discrete distributions.     

A semi-parametric estimation of a survival function from incomplete and doubly censored data

The purpose of this paper is to present a semi-parametric estimation of a survival function when analyzing incomplete and doubly censored data. Under the assumption that the chance of censoring is not related to the individual's survivorship, we propose a consistent estimation of survival. The derived estimator treats the uncensored observations nonparametrically and uses parametric models for both right and left censored data. Some asymptotic properties and simulation studies are also presented in order to analyze the behavior of the proposed estimator.     

Robustness of the student t based M-estimator

This paper considers the maximum likelihood type (M) estimator based on Student's t distribution for the location/scale model. The Student t M-estimator is generally thought to be robust to outliers. This paper shows that this is only true if the degrees of freedom parameter is kept fixed. By contrast, if the degrees of freedom parameter is also estimated from the data, the influence functions for the scale and degrees of freedom parameter become unbounded. Moreover, the influence function of the location parameter remains bounded, but its change-of-variance function is unboi~nded. The intuitioil behind these results is explained in the paper. The rates at which both the influence functions and the change-of-variance function diverge to infinity, are very slow. Tliis implies that outliers have to be extremely large in order to become detrimental to the performance of the Student t based M-estimator with estimated degrees of freedom. The theoretical results are illustrated in a a simulation experiment using several related competing estimators and several distributions for the error process.     

The roles of prior catchability assumptions and sample features on bayes estimates of the number of classes in a population

The object of this paper is to explain the role played by the catchability and sampling in the Bayesian estimation of k, the unknown number of classes in a multinomial population. It is shown that the posterior distribution of k increases as the capture probabilities of the classes become more unequal, and that the posterior distribution of k increases with the number of classes observed in the sample and decreases with the sample size. Moreover, it is shown that the posterior mean of k is consistent.     

Fuzzy Autoregressive Rules: Towards Linguistic Time Series Modeling

Fuzzy rule–based models, a key element in soft computing (SC), have arisen as an alternative for time series analysis and modeling. One difference with preexisting models is their interpretability in terms of human language. Their interactions with other components have also contributed to a huge development in their identification and estimation procedures. In this article, we present fuzzy rule–based models, their links with some regime-switching autoregressive models, and how the use of soft computing concepts can help the practitioner to solve and gain a deeper insight into a given problem. An example on a realized volatility series is presented to show the forecasting abilities of a fuzzy rule–based model.     

A Nonparametric Test for Symmetry Based on Freeman and Halton's Ideas on Contingency Tables

In this article, we propose a nonparametric method to test for symmetry in bivariate data. By using the extension of Fisher's exact treatment for 2 × 2 contingency tables proposed by Freeman and Halton (1951 Freeman , G. H. , Halton , J. H. ( 1951 ). Note on an exact treatment of contingency tables, goodness of fit and other problems of significance . Biometrika 38 : 141 – 149 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), we can test the hypothesis of equal distribution for two samples of integer valued variables. Then, by counting the number of observations belonging to each cell of a symmetric, appropriately built grid, we can produce the two samples of integers required to use this test for equal distribution. The resulting test for symmetry is potentially extendible to higher dimensions. A simulation study is performed to compare with some known tests (Bowker, 1948 Bowker , A. H. ( 1948 ). A test for symmetry in contingency tables . Journal of the American Statistical Association 43 : 572 – 574 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]; Hollander, 1971 Hollander , M. ( 1971 ). A nonparametric test for bivariate symmetry . Biometrika 58-1 : 203 – 212 .[Crossref], [Web of Science ®] , [Google Scholar]; and its improvement given in Krampe and Kuhnt, 2007 Krampe , A. , Kuhnt , S. ( 2007 ). Bowker's test for symmetry and modifications within the algebraic framework . Computational Statistics and Data Analysis 51 : 4124 – 4142 .[Crossref], [Web of Science ®] , [Google Scholar]). Our proposal represents a competitive option as a test for symmetry.     

Race, ethnicity, gender, and generational factors associated with the coming-out process among lesbian, and bisexual individuals

Age at coming out among gay/lesbian/bisexual (GLB) persons and sexual debut with same-gendered partners has typically been investigated in samples that do not reflect the racial and ethnic diversity of these communities. Addressing this limitation, data were collected from a diverse sample of men and women attending large-scale GLB community events in New York and Los Angeles in 2003 (N = 2,733). Compared to older cohorts, younger cohorts (18-24 year olds) of both men and women reported significantly earlier ages for sexual debut with same-gendered partners, and earlier ages for coming out to themselves and to others. Also, women began the process at later ages than men, as they reported coming out to themselves and sexual debut with a same-gender partner approximately two years later than men. There were no racial or ethnic differences in age out to self or others; however, persons of color were less likely to be out to their parents. Service providers, sexuality educators, and researchers should attend to the diversity in experience of coming out among GLB populations as they relate to the individuals gender, age, and racial and ethnic backgrounds.     

An employee assistance program for caregiver support

The Comprehensive Caregiver Choices Program provided support for employee caregivers of elderly people for employees at a hospital in Fort Worth, Texas. Key informant interviews and focus groups provided direction for program development and implementation. A full-time MSW and professionals with expertise in gerontology/geriatrics provided education and care coordination services to caregivers. Approximately 4% of the hospital's workforce participated in the program. Attendees evaluated educational sessions and follow-up interviews were conducted with program participants. Caregiver support programs must continue to seek innovative and creative marketing and service delivery methods to reach out and assist working caregivers in need of support.