× Distributions With Given Marginals and Statistical Modelling Close
Distributions With Given Marginals and Statistical Modelling by Carles M. Cuadras
English | PDF | 252 Pages | 2002 | ISBN : 9048161363 | 19.74 MB
As in the previous meetings, the theory of copulas has arelevant place in this book, as well as promising research on the more general concept of quasi- copulas. Other papers are devoted to the theory and compatibility of distri- butions, models for survival distributions and other well-known distributions. As was traditional in the previous meetings, several papers treat the problem of measuring dependence, monotonicity and ordering. A new set of papers is devoted to proposing some statistical models in aspects such as goodness of fit assessment, testing independence, estimating association parameters, etc.
The problem of existence, compatibility and construction of sets of distribu- tions with given marginals is, of course, a topic present in this meeting, as in the previous ones (Tiit).
Measuring dependence and other measures Measuring the separability of two distributions, with a multivariate extension, is useful in studying dependence and stochastic ordering (Kowa1czyk, Niewia- domska-Bugaj). The shape of a distribution belonging to a family, compared to another specified distribution (e.g., uniform), can be measured using the Wasserstein (also called Mallows) distance (Cuesta-Albertos, Matran, Rodri- guez). The dependence of a bivariate distribution can be measured by means of a concordance function Q. Thus Kendall, Spearman and Gini association coefficients can be measured using Q, which has a multivariate generalization (Nelsen). Monotonicity and stochastic ordering are probability notions with interest in statistics, and some derivations of them may not be equivalent (Fill, Machida). The closeness criteria between two distributions are useful in statis- tical estimation (Fountain).
Statistical modelling and inference
A multivariate survival distribution may be conditioned by a non-observable concomitant variable (Arnold, Beaver). Categorical models implicitly use ca- tegorical distributions and some restrictions on the marginals are analyzed (Bergsma). Some tests of independence may be improved by using princi- pal directions of each marginal variable (Cuadras). Time series models can be improved taking into account certain interactions within the marginals (Fried). Estimation of dependence in a copula can be approached taking the marginal distribution as nuisance parameters (Genest, Werker). A simple modification of Hoeffding' s maximum correlation can be used in goodness of fit assessment, with good results when compared to some classic tests (Fortiana, Grane). Para- metric copulas may provide a method for constructing a class of prior distribu- tions, but the dependence can have a strong influence on the posterior statistics (Murphy).i will be very grateful when you support me and buy Or Renew Your Premium from my Blog links
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