E cient stochastic data processing preassumes proper modeling of the statistics of the data source This paper addresses the issues that arise when the data to be pro cessed exhibits statistical properties which depart signi cantly from those implied under the Gaussianity assump tion This type of data has been found to be encountered in image speech and other compression applications For the cas...

Motivated from Computer Science problems we consider the following situation (compare [2] and [3]). In these papers the reader will find a more complete description as well as additional references. Let X denote a geometrically distributed random variable, i.e. P{X = k} = pqk−1 for k ∈ N and q = 1 − p. Assume that we have n independent random variables X1, . . . , Xn according to this distribut...

For words of length n, generated by independent geometric random variables, we consider the mean and variance, and thereafter the distribution of the number of runs of equal letters in the words. In addition, we consider the mean length of a run as well as the length of the longest run over all words of length n.

Let Sk be the k-th partial sum of Banach space valued independent identically distributed random variables. In this paper, we compare the tail distribution of ‖Sk‖ with that of ‖Sj‖, and deduce some tail distribution maximal inequalities. The main result of this paper was inspired by the inequality from [dP–M] that says that Pr(‖X1‖ > t) ≤ 5 Pr(‖X1 +X2‖ > t/2) whenever X1 and X2 are independent...

In undirected graphical models, each node represents a random variable while the set of edges specifies the conditional independencies of the underlying distribution. When the random variables are jointly Gaussian, the models are called Gaussian graphical models (GGMs) or Gauss Markov random fields. In this thesis, we address several important problems in the study of GGMs. The first problem is...

We derive strong laws of large numbers and central limit theorems for Bajraktarević, Gini exponential- (also called Beta-type) logarithmic Cauchy quotient means independent identically distributed (i.i.d.) random variables. The a sequence i.i.d. variables behave asymptotically normal with the usual square root scaling just like geometric given Somewhat surprisingly, multiplicative in rather dif...

In the literature of life-testing, general progressive censoring has been studied extensively. But, all the results have been developed under the key assumption that the units undertest are independently distributed. In this paper, we study general progressively Type-II censored order statistics arising from identical units under test which are jointly distributed according to an Archimedean co...