A Distribution of Class L Arising in the Theory of Risk
A factorisation of the Askey’s characteristic function
A free analogue of the transportation cost inequality on the circle
A functional inequality for the survival function of the gamma distribution.
A Gaussian correlation inequality and its applications to small ball probabilities.
A Gaussian Correlation Inequality for Certain Bodies in Rn .
A general purity law for convolution semigroups with discrete Levy measure.
A generalized beta function and associated probability density.
A generalized bivariate lifetime distribution based on parallel-series structures
In this paper, a generalized bivariate lifetime distribution is introduced. This new model is constructed based on a dependent model consisting of two parallel-series systems which have a random number of parallel subsystems with fixed components connected in series. The probability that one system fails before the other one is measured by using competing risks. Using the extreme-value copulas, the dependence structure of the proposed model is studied. Kendall's tau, Spearman's rho and tail dependences...
A generalized Kahane-Khinchin inequality
The inequality with an absolute constant C, and similar ones, are extended to the case of belonging to an arbitrary normed space X and an arbitrary compact group of unitary operators on X instead of the operators of multiplication by .
A generalized logistic distribution.
A generalized Ostrowski type inequality for a random variable whose probability density function belongs to .
A generalized residual information measure and its properties.
A geometric approach to correlation inequalities in the plane
By elementary geometric arguments, correlation inequalities for radially symmetric probability measures are proved in the plane. Precisely, it is shown that the correlation ratio for pairs of width-decreasing sets is minimized within the class of infinite strips. Since open convex sets which are symmetric with respect to the origin turn out to be width-decreasing sets, Pitt’s Gaussian correlation inequality (the two-dimensional case of the long-standing Gaussian correlation conjecture) is derived...
A geometrical approach to the special stable distributions
A geometry on the space of probabilities (II). Projective spaces and exponential families.
In this note we continue a theme taken up in part I, see [Gzyl and Recht: The geometry on the class of probabilities (I). The finite dimensional case. Rev. Mat. Iberoamericana 22 (2006), 545-558], namely to provide a geometric interpretation of exponential families as end points of geodesics of a non-metric connection in a function space. For that we characterize the space of probability densities as a projective space in the class of strictly positive functions, and these will be regarded as a...
A Hájek-Rényi-type maximal inequality and strong laws of large numbers for multidimensional arrays.
A limit theorem for the moment of self-normalized sums.
A log-Sobolev type inequality for free entropy of two projections
We prove a kind of logarithmic Sobolev inequality claiming that the mutual free Fisher information dominates the microstate free entropy adapted to projections in the case of two projections.
A maximal inequality for martingale local times