Traffic measurements from communication networks have shown that many quantities charecterizing network performance have long-tail probability distributions, i.e., with tails that decay more slowly than exponentially. File lengths, call holding times, scene lengths in MPEG video streams, and intervals between connection requests in Internet traffic all have been found to have long-tail distribu...

Heavy-tailed or power-law distributions are becoming increasingly common in biological literature. A wide range of biological data has been fitted to distributions with heavy tails. Many of these studies use simple fitting methods to find the parameters in the distribution, which can give highly misleading results. The potential pitfalls that can occur when using these methods are pointed out, ...

This short course covers the application of the statistical theory of extreme values to climate, in general, and to climate change, in particular. The statistical theory of extreme values is briefly reviewed, both the extremal types theorem with its application via the block maxima approach (i.e., fitting the generalized extreme value distribution) and the point process model with its applicati...

The Cloud Absorption Radiometer (CAR) was flown aboard the University of Washington Convair 580 (CV-580) research aircraft during the Chesapeake Lighthouse and Aircraft Measurements for Satellites (CLAMS) field campaign and obtained measurements of bidirectional reflectance distribution function (BRDF) of the ocean in July and August 2001 under different illumination conditions with solar zenit...

Recently, electron microscopy measurement of single particles has enabled us to reconstruct a low-resolution 3D density map of large biomolecular complexes. If structures of the complex subunits can be solved by x-ray crystallography at atomic resolution, fitting these models into the 3D density map can generate an atomic resolution model of the entire large complex. The fitting of multiple sub...

We are concerned with the estimation of the exterior surface and interior summaries of tube-shaped anatomical structures. This interest is motivated by two distinct scientific goals, one dealing with the distribution of HIV microbicide in the colon and the other with measuring degradation in white-matter tracts in the brain. Our problem is posed as the estimation of the support of a distributio...

Estimation of Maximum Flood Discharge (MFD) for a given return period is important for planning, design and management of hydraulic structures for the project. This can be achieved through Flood Frequency Analysis (FFA) by fitting of probability distributions to the recorded Annual Maximum Discharge (AMD) data. In this paper, Gamma and Extreme Value family of probability distributions are adopt...

We investigate the mis-match in the classical interpretation of certain distribution-fitting problems as maximum-likelihood (ML) estimation problems in the particular case of the I-divergence. The general relation between Bregman divergences and exponential families shown by Banerjee et al. [8] enables to consider distribution-fitting problems based on Bregman divergences as ML problems based o...

The web graph is a commonly-used network representation of the hyperlink structure of a website. A network of similar structure to the web graph, which we call the session graph has properties that reflect the browsing habits of the agents in the web server logs. In this paper, we apply session graphs to compare the activity of humans against web robots or crawlers. Understanding these properti...