We show that the number of individuals selecting their worst alternatives within a finite set of alternatives can be written as an alternating sum of the number of individuals having their best choice within subset of alternatives. The identities are then applied to random utility models,...

When assessing maps consisting of comparable regional values, it is of interest to know whether the peak, or maximum value, is higher than it would likely be by chance alone. Peaks on maps of crime or disease might be attributable to random fluctuation, or they might be due to an important...

Extreme value theory is the most scientific approach to an inherently difficult problem - predicting the possibility that an extreme event will occur. Broadly speaking, there are two kinds of models for extreme values. The first group of models are models for a distribution of normalized maximum...

Recent increase in intensity and frequency of catastrophic hydrologic events is shown to be a major threat to the global economy. These major events have been strongly linked to climate change and are expected to become worse in the future. The intensity-duration-frequency (IDF) curves quantify...

A generalization of the Gumbel distribution is presented to deal with general situations in modeling univariate data with broad range of skewness in the density function. This generalization is derived by considering a logarithmic transformation of an odd Weibull random variable. As a result,...

Graphical comparison of results for two or more groups or subsets can be accomplished by way of subdivision, superimposition, or juxtaposition. The choice between superimposition (several groups in one panel) and juxtaposition (several groups in several panels) can require fine discrimination:...