Operator geometric stable laws are the weak limits of operator normed and centered geometric random sums of independent, identically distributed random vectors. They generalize operator stable laws and geometric stable laws. In this work we characterize operator geometric stable distributions,...

Let {Xi, i[greater-or-equal, slanted]1} be a sequence of i.i.d. random vectors inRd, and let[nu]p, 0p1, be a positive, integer valued random variable, independent ofXis. The[nu]-stable distributions are the weak limits of properly normalized random sums [summation...

In this paper a class of limiting probability distributions of normalized sums of a random number of i.i.d. random variables is considered. The representation of such distributions via stable laws and asymptotic behavior of their moments and tail probabilities are established.

Multivariate Laplace distribution is an important stochastic model that accounts for asymmetry and heavier than Gaussian tails, while still ensuring the existence of the second moments. A Lévy process based on this multivariate infinitely divisible distribution is known as Laplace motion, and...

We introduce the notion of random self-decomposability and discuss its relation to the concepts of self-decomposability and geometric infinite divisibility. We present its connection with time series autoregressive schemes with a regression coefficient that randomly turns on and off. In...

We propose simple estimation of the location parameter for a density that is unbounded at the mode. The estimator maximizes a modified likelihood in which the singular term in the full likelihood is left out, whenever the parameter value approaches a neighborhood of the singularity location. The...

For given observations we consider the resampling distribution obtained by permuting residuals versus thedistribution of errors conditional on their order statistics. We observe thatwith high probabilityboth are approximately equal oncontrast vectorsafter suitable normalization. No...