Anderson's Theorem on the Integral of a Symmetric Unimodal Function over a Symmetric Convex Set, and Its Applications in Probability and Statistics

The Integral of a Symmetric Unimodal Function over a Symmetric Convex Set and Some Probability Inequalities

On a New Bimodal Normal Family

The unimodal distributions are frequently used in the theorical statistical studies. But in applied statistics, there are many situations in which the unimodal distributions can not be fitted to the data. For example, the distribution of the data outside the control zone in quality control or outlier observations in linear models and time series may require to be a bimodal. These situations, oc...

Extension of the Douady-Hubbard's Theorem on Connectedness of the Mandelbrot Set to Symmetric Polynimials

lVIULTIVARIATE PROBABILITY INEQUALITIES: CONVOLUTION THEORElVIS, COlVIPOSITION THEORElVlS, AND CONCENTRATION INEQUALITIES

Several important multivariate probability inequalities can be formulated in terms of multivariate convolutions of the form J!I (x )h(x (})dx, where usually !I = Ie is the indicator of a region C ~ R", h is a probability density on R , and (} is a translation parameter. Often fl and f2 possess convexity, monotonicity, and/or symmetry properties. More general multivariate compositions of the for...

Preclosure operator and its applications in general topology

In this paper, we show that a pointwise symmetric pre-isotonic preclosure function is uniquely determined the pairs of sets it separates. We then show that when the preclosure function of the domain is pre-isotonic and the pre-closure function of the codomain is pre-isotonic and pointwise-pre-symmetric, functions which separate only those pairs of sets which are already separated are precontinu...