The aim of this paper is to study the estimation of Pareto distribution on the basis of progressive type-II censored sample. First, the maximum likelihood estimator (MLE) is derived. Then the Bayes estimator of the unknown parameter of Pareto distribution is derived on the basis of Gamma prior distribution under entropy loss function. Further the empirical Bayes estimator also obtained by using...

Extending the notion of global search to multiobjective optimization is far than straightforward, mainly for the reason that one almost always has to deal with infinite Pareto optima and correspondingly infinite optimal values. Adopting Stephen Smale’s global analysis framework, we highlight the geometrical features of the set of Pareto optima and we are led to consistent notions of global conv...

In this paper we review the goodness-of-fit problem for assessing whether a sample is consistentwith the Pareto-type model. To this end we introduce a general kernel goodness-of-fit statistic. Thederivation of the proposed class is based on the close link between the strict Pareto and the exponentialdistribution and puts some of the available goodness-of-fit procedures for the latte...

We introduce a robust and asymptotically unbiased estimator for the tail index of Pareto-type distributions. The estimator is obtained by fitting the extended Pareto distribution to the relative excesses over a high threshold with the minimum density power divergence criterion. Consistency and asymptotic normality of the estimator is established under a second order condition on the distributio...

MULTI-OBJECTIVE OPTIMIZATION OF BLAST SIMULATION USING SURROGATE MODEL Toshihiro Tsuga, M.S. George Mason University, 2007 Thesis Director: Dr. Rainald Löhner A multi objective optimization approach using a Kriging model coupled with a Multi Objective Genetic Algorithm (MOGA) is applied to a blast damage maximization problem composed of two objectives, namely number of casualties and damage to ...

A new approach to goodness-of-fit for Pareto distributions is introduced. Based on Euclidean distances between sample elements, the family of statistics and tests is indexed by an exponent in (0,2) on Euclidean distance. The corresponding tests are statistically consistent and have excellent performance when applied to heavy-tailed distributions. The exponent can be tailored to the particular P...

Normally distributed data arises in various contexts and often one is interested in estimating its variance. The authors limit themselves in this chapter to the class of estimators that are (positive) multiples of sample variances. Two important qualities of estimators are bias and variance, which respectively capture the estimator’s accuracy and precision. Apart from the two classical estimato...

We propose a novel partial linearization based approach for optimizing the multi-class svm learning problem. Our method is an intuitive generalization of the Frank-Wolfe and the exponentiated gradient algorithms. In particular, it allows us to combine several of their desirable qualities into one approach: (i) the use of an expectation oracle (which provides the marginals over each output class...

Efficient experimental designs offer the potential to reduce confidence intervals for parameters of interest in choice models, or to reduce required sample sizes. C-efficiency recognises the salience of willingness to pay estimates rather than utility function parameters. This study reports on a choice model application that incorporated updated statistical designs based on initial responses in...