In this work we consider a power series of the form X=∑j=0∞δjZj where 0δ1 and {Zj}j≥0 is an i.i.d. sequence of random variables. We show that X is well-defined iff E[(log|Z0|)+]∞ and establish a number of properties of the distribution of X, such as continuity and closure under...

What is the distribution of the product of given powers of independent uniform (0, 1) random variables? Is this distribution useful? Is this distribution commonly used in some contexts? Is this distribution somehow related to the distribution of the product of other random variables? Are there...

The problem of determining the values of the independent variable given a value of the dependent variable is commonly referred to as the inverse regression problem. This problem is also encountered in real life with circular data and we refer to it in that context as the inverse circular...

Amato (1968) proposed using the length of the Lorenz curve as an index of inequality. The index has been little used, perhaps because of the perceived difficulty in analytically evaluating the value of the index in specific situations. A simple representation of the index as an expectation of a...

If X and Y are independent and if X+Y and X/(X+Y) are independent random variables, then X and Y must have gamma distributions. To confirm that lack of correlation between X and X/(X+Y) does not characterize the gamma distribution, a large class of distributions are identified for which...

Motivated by the observation that for a sample of size two from an exponential distribution, the largest order statistic is distributed as a convolution of two independent exponential random variables with distributions differing only in their intensity or rate parameter, a spectrum of related...

Two classes of k-dimensional distributions with generalized Pareto conditionals are characterized. This subsumes and extends earlier work on distributions with Pareto conditionals.