Much of the practical interest attached to curves and surfaces derives from features of roughness, rather than smoothness. For example, considerable attention has been paid to fractal models of curves and surfaces, for which the notions of a normal and curvature are usually not well defined....

By means of the Malliavin Calculus, we derive asymptotic expansion of the probability distributions of statistics for systems perturbed by small noises. These results are applied to the problem of the second order asymptotic efficiency of the maximum likelihood estimator.

A class of multivariate distributions that are mixtures of the positive powers of a max-infinitely divisible distribution are studied. A subclass has the property that all weighted minima or maxima belong to a given location or scale family. By choosing appropriate parametric families for the...

We concentrate attention on non-negative absolutely continuous random variables with aSchur-constantjoint survival function. Such a property defines a special case of exchangeability, corresponding to a multivariateno agingcondition, in a Bayesian set-up. In the longitudinal observation of our...

One of the aims of discriminant analysis is the allocation of unknown entities to populations that are knowna priori. Considerkpopulations. LetXdenote the vector of observations on an experimental unit, whose origin is uncertain. For the general parametric case, a test is proposed to verify the...

Some new results are obtained on stochastic orderings between random vectors of spacings from heterogeneous exponential distributions and homogeneous ones. LetD1, ..., Dnbe the normalized spacings associated with independent exponential random variablesX1, ...,Xn, whereXihas hazard...

We consider estimation and confidence regions for the parameters[alpha]and[beta]based on the observations (X1, Y1), ..., (Xn, Yn) in the errors-in-variables modelXi=Zi+eiandYi=[alpha]+[beta]Zi+fifor normal errorseiandfiof which the covariance matrix is known up to a constant. We...

In the univariate setup the Lomax distribution is being widely used for stochastic modelling of decreasing failure rate life components. It also serves as a useful model in the study of labour turnover, queueing theory, and biological analysis. A bivariate extension of the Lomax distribution...

Majumdar (1994, J. Multivariate Anal.48 87-105) compounds (in the sense of Robbins, 1951, "Proceedings, Second Berkeley Sympos. Math. Statist. Probab.," pp. 131-148, Univ. of California Press, Berkeley) the estimation problem in the mean-parameter family of Gaussian distributions on a real...

Let X1, ..., Xn be independent identically distributed observations from an unknown probability density f(·), such that its support G = supp f is a subset of the unit square in 2. We consider the problem of estimating G from the sample X1, ..., Xn, under the assumption that the boundary of G...