Two concepts of symmetry for the distributions of positive random variables Y are log-symmetry (symmetry of the distribution of log Y ) and Rsymmetry (Mudholkar & Wang, 2007). In this paper, we characterise the distributions that have both properties, which we call doubly symmetric. It turns out that doubly symmetric distributions constitute a subset of those distributions that are moment-equiv...

The distribution function of a sum of lognormal random variables appears in several communication problems. Approximations are usually used for such distribution as no closed form nor bounds exist. Bounds can be very useful in assessing the performance of any given system. In this paper, we derive upper and lower bounds on the distribution function of a sum of independent lognormal random varia...

A procedure is presented in this paper for developing a representation of lognormal stochastic processes via the polynomial chaos expansion. These are processes obtained by applying the exponential operator to a gaussian process. The Polynomial Chaos expansion results in a representation of a stochastic process in terms of mul-tidimensional polynomials orthogonal with respect to the Gaussian me...

The aim of this paper is to present two moment matching procedures for basketoptions pricing and to test its distributional approximations via distances on the space of probability densities, the Kullback-Leibler information (KLI) and the Hellinger distance (HD). We are interested in measuring the KLI and the HD between the real simulated basket terminal distribution and the distributions used ...

In this paper, we consider admissible estimation of the parameter ?r in the gamma distribution with truncated parameter space under entropy loss function. We obtain the classes of admissible estimators. The result can be applied to estimation of parameters in the normal, lognormal, pareto, generalized gamma, generalized Laplace and other distributions.

Using probability plots and Maximum Likelihood Estimation (MLE), we fit lognormal distributions to data compiled by Ershow et al. for daily intake of total water and tap water by three groups of women (controls, pregnant, and lactating; all between 15-49 years of age) in the United States. We also develop bivariate lognormal distributions for the joint distribution of water ingestion and body w...