Distributions of the ratios of independent beta variables and applications

We establish the exact expressions of X₁/X₂ and of X₁/(X₁+X₂), where X₁ and X₂ are independent beta random variables of the first type, and provide some of their applications, in reliability and availability.     

Critical issues on informed consent in Africa

Biomedical research has made tremendous advances during the last decade in improving human health and well being. In spite of these advances, research has encountered serious emerging challenges as it moves across boarders and confronts different societies with different cultural practices, beliefs, moral thoughts and different values. A pervasive and perplexing issue affecting the current advances in research is the perception that research might end up exploiting populations unless it is conducted in the context of a strong ethical framework. Furthermore, informed consent has increasingly become a thorny area for researchers when considering what should be done when introducing the process into a community, especially if the process might destroy the traditional value system and customs of the community. In this paper, I argue that community consent is an unethical process which should be subverted for community dialogue and community education in research in Africa.     

Sex,Arts and Verbal Abilities: Three Further Indicators of How American Life is not Improving

Despite clear evidence that Americans’ economic standard of living has improved over the last half-century in terms of income, ownership of technology and housing among other indicators, there is scant evidence from non-economic quality-of-life (QOL) indicators of improved life quality to parallel these economic gains. The present article adds to this list in showing little if any progress in three QOL indicators (the first two about time and activity) that have received less or no attention in the social indicators literature, namely (1) frequency of the highly enjoyable activity of sex, (2) participation in various serious arts activities and (3) scores of verbal ability. The data on sexual activity and verbal ability come from the 1974–2008 General Social Surveys (GSS) from the University of Chicago, and for the arts from the 2008 Survey of Public Participation in the Arts (SPPA) conducted by the US Census Bureau for the National Endowment for the Arts since 1982. All three surveys interviewed nationally representative samples, with over 70% response rates and sample sizes of more than 15,000 adults. The GSS data on sexual frequency show no significant increase in estimated frequency of sex since 1989, despite its strong appeal and the availability of new societal conveniences. This held both before and after adjustment for the age, marital status and education in the population; contrary to expectation, working long hours was associated with increased sex both before and after adjustment for these other demographic predictors. The SPPA trend data on arts participation actually showed a decline in participation, especially after adjustment for its major predictor of years of education; again no decreased participation was found among those working long hours. While scores on verbal ability in the GSS have stayed rather steady since 1974, they have decreased after MCA adjustment for the increased college education in more recent years, as documented by Nie et al. (2009). Thus, contrary to expectations, increases in public education have not been accompanied by improvements on these three indicators.     

Estimation of gaussian mixtures with rotationally invariant covariance matrices

Homoscedastic and heteroscedastic Gaussian mixtures differ in the constraints placed on the covariance matrices of the mixture components. A new mixture, called herein a strophoscedastic mixture, is defined by a new constraint, This constraint requires the matrices to be identical under orthogonal trans¬formations, where different transformations are allowed for different matrices. It is shown that the M-step of the EM method for estimating the parameters of strophoscedastic mixtures from sample data is explicitly solvable using singular value decompositions. Consequently, the EM-based maximum likelihood estimation algorithm is as easily implemented for strophoscedastic mixtures as it is for homoscedastic and heteroscedastic mixtures. An example of a “noisy” Archimedian spiral is presented.     

A perspective of composite sampling

Composite samples are formed by physically mixing samples. Usually, composite samples are used to reduce the overall cost associated with analytical procedures that must be performed on each sample, but they can also be used to protect the privacy of individuals.

Composite sampling can reduce the cost of identifying individual cases that have a certain trait, such as those with a rare disease or those exceeding pollution-level standards. Not much is lost by applying this method as long as the trait is relatively rare.

Composite sampling can reduce the cost of estimating the mean of some process. When samples are composited, the ability to estimate the variance is lost. In spite of this, the potential savings are so great that composite samples have been used.

Much of this paper deasl with the variance of estimators based on composite sampling when the porportions of hte original samples comprising the composite sample are actually random. Taking repeated samples and measurements on several composite samples complicates the prodcedure, but allows the estimation of between and within variation as well as measurement error.     

An F Approximation to the Distribution of a Linear Combination of Chi-squared Variables.

A three-parameter F approximation to the distribution of a positive linear combination of central chi-squared variables is described. It is about as easy to implement as the Satterthwaite-Welsh and Hall-Buckley-Eagleson approximations. Some reassuring properties of the F approximation are derived, and numerical results are presented. The numerical results indicate that the new approximation is superior to the Satterthwaite approximation and, for some purposes, better than the Hall-Buckley-Eagleson approximation. It is not quite as good as the Gamma-Weibull approximation due to Solomon and Stephens, but is easier to implement because iterative methods are not required.     

Sexual Frequency and the Stability of Marital and Cohabiting Unions

Prior research found that lower sexual frequency and satisfaction were associated with higher rates of divorce, but little research had examined the role of sexual activity in the dissolution of cohabiting unions. We drew upon social exchange theory to hypothesize why sexual frequency is more important in cohabitation: (a) cohabitors' lower costs of finding sexual alternatives, (b) cohabitors' lower barriers to ending the relationship in the form of union‐specific economic and noneconomic capital, and (c) cohabitors' higher expectations for sexual activity. Using the National Survey of Families and Households (N = 5,902), we examined the relationship between sexual frequency and union dissolution. Results indicated that low sexual frequency was associated with significantly higher rates of union dissolution among cohabitors than married couples.     

Fractional replication in simulation studies

It is shown how to use fractional replication in simulation studies. Examples are given. Considerable savings in number of runs required can be achieved through the use of fractional replication ideas.