Transmuted generalized exponential distribution: A generalization of the exponential distribution with applications to survival data

In this article, we investigate the potential usefulness of the three-parameter transmuted generalized exponential distribution for analyzing lifetime data. We compare it with various generalizations of the two-parameter exponential distribution using maximum likelihood estimation. Some mathematical properties of the new extended model including expressions for the quantile and moments are investigated. We propose a location-scale regression model, based on the log-transmuted generalized exponential distribution. Two applications with real data are given to illustrate the proposed family of lifetime distributions.     

Effects of some design factors on the distribution of similarity indices in cluster analysis

This article investigates the effects of number of clusters, cluster size, and correction for chance agreement on the distribution of two similarity indices, namely, Jaccard and Rand indices. Skewness and kurtosis are calculated for the two indices and their corrected forms then compared with those of the normal distribution. Three clustering algorithms are implemented: complete linkage, Ward, and K-means. Data were randomly generated from bivariate normal distributions with specified means and variance covariance matrices. Three-way ANOVA is performed to assess the significance of the design factors using skewness and kurtosis of the indices as responses. Test statistics for testing skewness and kurtosis and observed power are calculated. Simulation results showed that independent of the clustering algorithms or the similarity indices used, the interaction effect cluster size x number of clusters and the main effects of cluster size and number of clusters were found always significant for skewness and kurtosis. The three way interaction of cluster size x correction x number of clusters was significant for skewness of Rand and Jaccard indices using all clustering algorithms, but was not significant using Ward's method for both Rand and Jaccard indices, while significant for Jaccard only using complete linkage and K-means algorithms. The correction for chance agreement was significant for skewness and kurtosis using Rand and Jaccard indices when complete linkage method is used. Hence, such design factors must be taken into consideration when studying distribution of such indices.     

Family Economy,Rural School Choice,and Flexischooling Children with Disabilities

Most homeschooled students would be more accurately described as “flexischooled,” partly homeschooled and partly enrolled in school. The popularity of these two alternatives to public or private school enrollment has increased over the past several decades to the extent that, by 2012 over 2 million students, 4 percent of the population, were either flexischooled or homeschooled in the United States. To understand why parents have pursued these options over enrollment, we employed a family economy perspective, arguing that family, child, and locational considerations shaped parents' motivations for homeschooling or flexischooling over enrollment. For example, parents' decisions were partially shaped by the interaction between children's disability status and rural location. Using data from the National Household Education Survey 2012, this article first describes the prevalence of flexischooling and full‐time homeschooling. Then, it demonstrates how various family, child, and locational factors shape the odds of flexischooling and homeschooling, and then examines the interaction between location and children's disability status in detail. We discuss the implications of our findings for family economy theoretical perspectives, flexischooling, and rural education research.     

Accelerometry analysis of physical activity and sedentary behavior in older adults: a systematic review and data analysis

Accelerometers objectively monitor physical activity and sedentary patterns and are increasingly used in the research setting. It is important to maintain consistency in data analysis and reporting, therefore, we: (1) systematically identified studies using accelerometry (ActiGraph, Pensacola, FL, USA) to measure moderate-to-vigorous physical activity (MVPA) and sedentary time in older adults, and (2) based on the review findings, we used different cut-points obtained to analyze accelerometry data from a sample of community-dwelling older women. We identified 59 articles with cut-points ranging between 574 and 3,250 counts/min for MVPA and 50 and 500 counts/min for sedentary time. Using these cut-points and data from women (mean age, 70 years), the median MVPA minutes per day ranged between 4 and 80 min while percentage of sedentary time per day ranged between 62 % and 86 %. These data highlight (1) the importance of reporting detailed information on the analysis assumptions and (2) that results can differ greatly depending on analysis parameters.     

Selective Maintenance in System Reliability with Random Costs of Repairing and Replacing the Components

In this paper we consider the problem of determining the optimum number of repairable and replaceable components to maximize a system's reliability when both, the cost of repairing the components and the cost of replacement of components by new ones, are random. We formulate it as a problem of non-linear stochastic programming. The solution is obtained through Chance Constrained programming. We also consider the problem of finding the optimal maintenance cost for a given reliability requirement of the system. The solution is then obtained by using Modified E-model. A numerical example is solved for both the formulations.     

Testing base load with non-sample prior information on process load

Inference about population parameters could be improved using non- sample prior information (NSPI) from reliable sources along with the available data. This paper studies the problem of testing the intercept parameter of a simple regression model when NSPI is available on the value of the slope. The information on the slope may have the three different scenarios: (i) unknown (unspecified), (ii) known (certain or specified), and (iii) uncertain if the suspected value is unsure, for which we define the unrestricted test (UT), restricted test (RT) and pre-test test (PTT) for the intercept parameter. The test statistics, their sampling distributions, and power functions are derived. Comparison of the power functions and size of the tests are used to search and recommend a best test. The study reveals that the PTT has a reasonable dominance over the UT and RT both in terms of achieving highest power and lowest size.     

Estimation of the intercept parameter for linear regression model with uncertain non-sample prior information

This paper considers alternative estimators of the intercept parameter of the linear regression model with normal error when uncertain non-sample prior information about the value of the slope parameter is available. The maximum likelihood, restricted, preliminary test and shrinkage estimators are considered. Based on their quadratic biases and mean square errors the relative performances of the estimators are investigated. Both analytical and graphical comparisons are explored. None of the estimators is found to be uniformly dominating the others. However, if the non-sample prior information regarding the value of the slope is not too far from its true value, the shrinkage estimator of the intercept parameter dominates the rest of the estimators.