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 study aims to estimate the parameter of the Generalized Pareto Distribution under Type II censored samples. The Bayes Estimators have been derived under a class of informative and non-informative Priors using different symmetric and asymmetric Loss functions. The Credible Intervals, Highest Posterior Density (HPD) intervals, Posterior Predictive Distributions and Posterior Predictive Interv...

We study nonsmooth multiobjective programming problems involving locally Lipschitz functions and support functions. Two types of Karush-Kuhn-Tucker optimality conditions with support functions are introduced. Sufficient optimality conditions are presented by using generalized convexity and certain regularity conditions. We formulate Wolfe-type dual and Mond-Weirtype dual problems for our nonsmo...

We show that Tsallis’ distributions can be derived from the standard (Shannon) maximum entropy setting, by incorporating a constraint on the divergence between the distribution and another distribution imagined as its tail. In this setting, we find an underlying entropy which is the Rényi entropy. Furthermore, escort distributions and generalized means appear as a direct consequence of the cons...

Decomposition-based methods are often cited as the solution to multi-objective nonconvex optimization problems with an increased number of objectives. These methods employ a scalarizing function to reduce the multi-objective problem into a set of single objective problems, which upon solution yield a good approximation of the set of optimal solutions. This set is commonly referred to as Pareto ...

Dihedral filters correspond to the Fourier transform of functions defined on square grids. For gray value images there are six pairs of dihedral edge-detector pairs on 5x5 windows. In low-level image statistics the Weibullor the generalized extreme value distributions are often used as statistical distributions modeling such filter results. Since only points with high filter magnitudes are of i...

This paper studies a class of social welfare relations (SWRs) on the set of infinite utility streams. In particular, we examine the SWRs satisfying Q-Anonymity, an impartiality axiom stronger than Finite Anonymity, as well as Strong Pareto and a certain equity axiom. First, we characterize the extension of the generalized Lorenz SWR by combining Q-Anonymity with Strong Pareto and Pigou-Dalton E...

In this paper, we give some new generalized convexities with the tool–right upper-Diniderivative which is an extension of directional derivative. Next, we establish not only Karush-KuhnTucker necessary but also sufficient optimality conditions for mathematical programming involving new generalized convex functions. In the end, weak, strong and converse duality results are proved to relate weak ...