Recurrence relations for moments of different orders of extremes from gamma distribution

Certain recurrence relations for the moments of different orders of the largest order statistic from a gamma distribution with shape parameter p are obtained. By using this it is shown that for obtaining the moment of any order of each order statistic of a sample of size n from the gamma distribution, one has to evaluate at most n-2 single integrals.     

The sociolinguistics of exogamy: Dialect acquisition in a Zhuang village

Adult dialect acquisition is typically studied in relatively idiosyncratic situations where adults happen to move to another community. But how does dialect acquisition play out in indigenous minority societies that have systemic adult migration due to exogamy? Do the in‐married spouses acquire the local variety? Why or why not? How much do they acquire? We investigated an indigenous Zhuang community in southern China. Sociophonetic analyses of in‐married women and local villagers show that the in‐married women acquired the local variety in most respects but not in aspirated consonants. To the limits of their phonological ability as adult learners, the wives followed the local sociolinguistic norm: they acquired the husbands’ variety. By contrast, in societies experiencing greater external cross‐cultural contact, exogamous women sometimes use their liminal status to challenge such gendered sociolinguistic expectations. Comparing the present study with outcomes in different societies, we lay the foundation for a typology of the sociolinguistics of exogamy. In this way, we help expand the study of language and gender toward new horizons and under‐represented social settings.     

Costs,Benefits, and Management Considerations of a Prepaid Student Dental Health Plan

Abstract

The Student Dental Health Program (SDHP) is an open panel, prepaid dental insurance plan at the University of Alabama in Birmingham. The program was developed primarily to provide optimal dental health service; however the SDHP also serves educational and research functions that are consistent with the objectives of the university. The student bodies of the Schools of Dentistry, Medicine, Nursing, and Optometry constitute the enrollee population.

Total cost rose from $18,418 in 1969–70 with 862 enrollees, to $70,930 in 1975–76 with 1,618 enrollees. During the same period the number of procedures completed increased from 2,868 to 6,796, with the average cost per procedure increasing from $6.42 to $10.44. The number of restorative services declined and preventive services increased. In 1976–77 benefits per student treated were estimated at $80 as compared to the annual fee of $48. The value of unmet needs upon entrance to the program averaged $59 per enrollee in 1974–75. By 1976–77 this figure was reduced to $26 due to implementation of an initial screening. The program is self-supporting due to a variety of cost containment measures. On balance, the program can be considered successful and beneficial to all parties concerned.     

Large Differences between Partial Correlation Coefficients

A plot of each ranking of N objects in N-dimensional space is shown to provide geometric interpretations of Kendall's tau and Spearman's rho and also of the relationship of rho to a sum of inversion weights. The computation of rho from a sum of inversion weights is shown to allow sequential calculation of rho.     

A Mechanical Interpretation of the Coefficient of Rank Correlation and other Analogies

Periodically, the pyramid or “chain letter” scheme is offered to Americans under the guise of a business dealership. Recently, the FTC ordered Glen Turner's “Dare to be Great” firm to repay 44 million dollars to participants. In order to demonstrate that the potential gains are misrepresented by promoters, a probability model of the pyramid scheme is developed. The major implications are that the vast majority of participants have less than a ten percent chance of recouping their initial investment when a small profit is achieved as soon as they recruit three people and that, on the average, half of the participants will recruit no one else and lose all their money.     

Correlation Coefficient Revisited

Elementary approaches to prove basic properties of the correlation coefficient are of pedagogical interest. Besides posing another proof, this article gives variations of the proofs already existing in the statistical literature     

An Improved Boxplot for Univariate Data

The boxplot is an effective data-visualization tool useful in diverse applications and disciplines. Although more sophisticated graphical methods exist, the boxplot remains relevant due to its simplicity, interpretability, and usefulness, even in the age of big data. This article highlights the origins and developments of the boxplot that is now widely viewed as an industry standard as well as its inherent limitations when dealing with data from skewed distributions, particularly when detecting outliers. The proposed Ratio-Skewed boxplot is shown to be practical and suitable for outlier labeling across several parametric distributions.     

Simulation of the p-generalized Gaussian distribution

In this paper, we introduce the p-generalized polar methods for the simulation of the p-generalized Gaussian distribution. On the basis of geometric measure representations, the well-known Box–Muller method and the Marsaglia–Bray rejecting polar method for the simulation of the Gaussian distribution are generalized to simulate the p-generalized Gaussian distribution, which fits much more flexibly to data than the Gaussian distribution and has already been applied in various fields of modern sciences. To prove the correctness of the p-generalized polar methods, we give stochastic representations, and to demonstrate their adequacy, we perform a comparison of six simulation techniques w.r.t. the goodness of fit and the complexity. The competing methods include adapted general methods and another special method. Furthermore, we prove stochastic representations for all the adapted methods.