Building on ideas and concepts introduced by Lad, Taylor and Hosking, a generalized Cantor distribution and a corresponding skew generalized Cantor distribution are developed and analyzed. Associated inverse distributions are also introduced. In some cases method of moment estimation is shown to...

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...

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...

Suppose (X,Y) has a (k+1)-dimensional Cauchy distribution. Consider the conditional distribution of X given Yy0, for some fixed value of . The resulting distribution is the multivariate skewed Cauchy, in which there is truncation with respect to Y: this is but one of a general class of skewed...

Let {Yn} be a sequence of i.i.d. non-negative extended real valued random variables. For c 0, consider stationary stochastic processes of the form Xn = c min(Xn-1, Yn). Subject to a regularity condition related to the behavior of FYn(y) in a neighborhood of 0, it is verified that the associated...

This paper uses an extension of a theorem of Polya to derive bounds for the variance of a random variable. These are applied to maxima and minima of a sample and the bounds are found to be quite good.

Suppose that a system consists of n independent components and that the lifelength of the ith component is a random variable . For k[set membership, variant]{1,2,...,n-1}, denote by , the residual lifelengths of the remaining functioning components following the kth failure in the system. We...