A revisit to test the equality of variances of several populations

We revisit the problem of testing homoscedasticity (or, equality of variances) of several normal populations which has applications in many statistical analyses, including design of experiments. The standard text books and widely used statistical packages propose a few popular tests including Bartlett's test, Levene's test and a few adjustments of the latter. Apparently, the popularity of these tests have been based on limited simulation study carried out a few decades ago. The traditional tests, including the classical likelihood ratio test (LRT), are asymptotic in nature, and hence do not perform well for small sample sizes. In this paper we propose a simple parametric bootstrap (PB) modification of the LRT, and compare it against the other popular tests as well as their PB versions in terms of size and power. Our comprehensive simulation study bursts some popularly held myths about the commonly used tests and sheds some new light on this important problem. Though most popular statistical software/packages suggest using Bartlette's test, Levene's test, or modified Levene's test among a few others, our extensive simulation study, carried out under both the normal model as well as several non-normal models clearly shows that a PB version of the modified Levene's test (which does not use the F-distribution cut-off point as its critical value), and Loh's exact test are the “best” performers in terms of overall size as well as power.     

A general approximation to quantiles

For many continuous distributions, a closed-form expression for their quantiles does not exist. Numerical approximations for their quantiles are developed on a distribution-by-distribution basis. This work develops a general approximation for quantiles using the Taylor expansion. Our method only requires that the distribution has a continuous probability density function and its derivatives can be derived to a certain order (usually 3 or 4). We demonstrate our unified approach by approximating the quantiles of the normal, exponential, and chi-square distributions. The approximation works well for these distributions.     

The Condom Fairy program: A novel mail-order service for condoms and sexual health supplies

Abstract

Objective: In recent years college health professionals have used a variety of innovative strategies to increase availability and accessibility of condoms and safer sex products. The purpose of this study is to evaluate the efficacy and efficiency of a mail-order delivery program titled the Condom Fairy. Participants: Seven hundred thirty-three students (63.4% women, 86.1% heterosexual, and 59.2% Caucasian) completed a questionnaire assessing their overall experience with the program. Methods: Participants completed a 60 item questionnaire 30?days after receiving condoms and safer sex products. Results: Overall, 46,980 condoms were distributed over a six semester period. Almost all of the participants (97.4%) reported they ordered male condoms while 58.0% ordered sexual lubricant, 11.1% female condoms, and 10.2% latex dams. Nearly than three-quarters (73.9%) of participants reported they used the condoms provided. Conclusions: Findings support the implementation of innovative mail-in condom and safer sex product programs on college campuses.     

Inverse gaussian accelerated test models based on cumulative damage

The failure of a system under environmental stress often can be described by an accelerated test model which incorporates the environmental variable L. Here, the failure of such a system at environmental level L is modeled as the first passage of accumulated damage to a critical threshold value. Assuming a discrete additive damage model leads to a Birnbaum–Saunders-type distribution for the failure time which can be closely approximated by an inverse Gaussian-type model. However, if a continuous damage model based on a Gaussian process is assumed, a more general family of inverse Gaussian accelerated test models is obtained. Three sets of failure data are discussed to illustrate the usefulness of this general family.     

A non-iterative posterior sampling algorithm for linear quantile regression model

In this article, a non-iterative posterior sampling algorithm for linear quantile regression model based on the asymmetric Laplace distribution is proposed. The algorithm combines the inverse Bayes formulae, sampling/importance resampling, and the expectation maximization algorithm to obtain independently and identically distributed samples approximately from the observed posterior distribution, which eliminates the convergence problems in the iterative Gibbs sampling and overcomes the difficulty in evaluating the standard deviance in the EM algorithm. The numeric results in simulations and application to the classical Engel data show that the non-iterative sampling algorithm is more effective than the Gibbs sampling and EM algorithm.     

A multiple warm standby δ-shock system with a repairman having multiple vacations

In this article, a warm standby n-unit system is studied. The system is operational as long as there is one unit normal. The unit online, which has a lifetime distribution governed by a phase-type distribution, is also attacked by a shock from some external causes. Assume that shocks arrive according to a Poisson process. Whenever an interarrival time of shock is less than a threshold, the unit online fails. The lifetimes of the units in warm standby is exponentially distributed. A repairman who can take multiple vacations repairs the failed units based on the “first-in-first-out” rule. The repair times and the vacation times of repairman are governed by different phase-type distributions. For this system, the Markov process governing the system is constructed. The system is studied in a transient and stationary regime; the availability, the reliability, the rates of occurrence of the different types of failures, and the working probability of the repairman are calculated. A numerical application is performed to illustrate the calculations.     

Shared frailty model based on reversed hazard rate for left censored data

Frailty models are used in the survival analysis to account for the unobserved heterogeneity in the individual risks to disease and death. To analyze the bivariate data on related survival times (e.g., matched pairs experiments, twin or family data), the shared frailty models were suggested. In this article, we introduce the shared gamma frailty models with the reversed hazard rate. We develop the Bayesian estimation procedure using the Markov chain Monte Carlo (MCMC) technique to estimate the parameters involved in the model. We present a simulation study to compare the true values of the parameters with the estimated values. We apply the model to a real life bivariate survival dataset.     

Micro‐investment perspective and the potential of the universal basic income

The article evaluates prospects of the Basic Income (BI) as a development policy tool. While BI is a relatively new initiative within development policy, the article argues that it should be seen as a serious option in the future, given the changing geography of poverty and the findings from existing cash transfer schemes. The analysis is carried out as a synthesis of existing findings on BI pilot programmes, along with cash transfer instruments more generally. While not including new empirical data, the synthesis allows preliminary estimates on the likely impacts of abolishing conditioning and targeting in cash transfer schemes. Particular attention is paid to the notion of micro‐investment and the psychological conditions of micro‐investment.     

Comparison between method of moments and entropy regularization algorithm applied to parameter estimation for mixed-Weibull distribution

Mixed-Weibull distribution has been used to model a wide range of failure data sets, and in many practical situations the number of components in a mixture model is unknown. Thus, the parameter estimation of a mixed-Weibull distribution is considered and the important issue of how to determine the number of components is discussed. Two approaches are proposed to solve this problem. One is the method of moments and the other is a regularization type of fuzzy clustering algorithm. Finally, numerical examples and two real data sets are given to illustrate the features of the proposed approaches.     

中国商品流通现代化的模糊综合评价研究

完善了商品流通现代化指标体系,并运用模糊综合法将商品流通现代化指标转换成了指数。研究发现商品流通现代化水平与其区域位置、总体经济实力密切相关,且受到产业结构的影响。同时,通过基于指数的聚类分析得到如下结论:"率先发展型区域"要抓住历史机遇,培养创新型人才,保持领先地位;"积极追赶型区域"要发挥地理优势,打破省之间、行业和部门之间、所有制之间的界限,积极参与各种区域经济合作;"流通欠发达型区域"要进一步推进和实施西部大开发战略,推进物流现代化。