Extreme-value statistics is often used to estimate so-called return values (actually related to quantiles) for environmental quantities like wind speed or wave height. A basic method for estimation is the method of block maxima which consists in partitioning observations in blocks, where maxima from each block could be considered independent.…

We implemented a synchronous distance course entitled: Introductory Finance designed for undergraduate students. This course was held between two Japanese universities. Stable Internet connections allowing minimum delay and minimum interruptions of the audio-video streaming signals were used. Students were equipped with their own PCs with…

There has been a lot of material written about logarithmic spirals of golden proportion but this author states that he has never come across an article that states the exact equation of the spiral which ultimately spirals tangentially to the sides of the rectangles. In this article, the author intends to develop such an equation. (Contains 5…

Each ellipse and hyperbola has a circle associated with it called the director circle. In this article, the author derives the equations of the circle for the ellipse and hyperbola through a different approach. Then the author concentrates on the director circle of the central conic given by the general quadratic equation. The content of this…

Because interest in catalysts is widespread, the kinetics of catalytic reactions have been investigated by widely diverse groups of individuals, including chemists, engineers, and biologists. This has lead to redundancy in theories, particularly with regard to the topics of homogeneous, heterogeneous, and enzyme catalysis. From a pedagogical…

The mean and variance of some continuous distributions, in particular the exponentially decreasing probability distribution and the normal distribution, are considered. Since they involve integration by parts, many students do not feel comfortable. In this note, a technique is demonstrated for deriving mean and variance through differential…

In this paper methods and algorithms for identifying the main elements (edges and facets of any dimension) of a cone and a polytope, and calculating the corresponding hypervolumes are presented. The cones and polytopes are supposed to be given as the non-negative linear combination and the convex hull generated by a, not necessarily minimal, set…

Coefficients of correlation and concordance are defined for profiles consisting of ensembles of partially ordered sets, by extending Kendall's rank order correlation (tau) and Kendall's coefficient of concordance (W) to cases where subjects are asked to rank order, or to choose among, the given alternatives in multiple sets of items. (Author/PN)

Under certain conditions, a validity Coefficient of Effective Length (CEL) can produce highly misleading results. A modified coefficent is suggested for use when empirical studies indicate that underlying assumptions have been violated. (Author/BW)

A more general method for calculating the Kappa measure of nominal rating agreement among multiple raters is presented. It can be used across a broad range of rating designs, including those in which raters vary with respect to their base rates and how many subjects they rate in common. (Author/BW)

Four separate approaches to the problem of assessing variation in categorical data are developed, each of which results in an identical index of dispersion. An additional index, related to a measure of entropy for categorical data, is mentioned and some applications are discussed. (Author/RL)

Power and stability of Type I error rates are investigated for the Box-Scheffe test of homogeneity of variance with varying subsample sizes under conditions of normality and nonnormality. The test is shown to be robust to violation of the normality assumption when sampling is from a leptokurtic population. (Author/GK)

Guilford's average interrater correlation coefficient is shown to be related to the Friedman Rank Sum statistic. Under the null hypothesis of zero correlation, the resultant distribution is known and the hypothesis can be tested. Large sample and tied score cases are also considered. An example from Guilford (1954) is presented. (Author)

The F-distribution approximation suggested by Dixon was investigated at various combinations of alpha and degrees of freedom. Tabled values were compared with values computed utilizing the suggested formula. (Author/GSK)

The value of the phi coefficient cannot, in general, be uniquely determined from the G index. G is more suitable than the phi coefficient as a measure of similarity between individuals, because phi is too unstable over item reflection. (Author/RL)