On Geometric Infinite Divisibility p-thinning and Cox Processes

We discuss the connections among geometric infinite divisibility, thinning of renewal processes and Cox processes in this paper.Comment: 7 pages. This paper had won the Young Scientists Award at the 77th session of the Indian Science Congress Association held at Cochin, January 199

Infinite Divisibility and Max-Infinite Divisibility with Random Sample Size

Continuing the study reported in Satheesh (2001),(math.PR/0304499 dated 01 May 2003) and Satheesh (2002)(math.PR/0305030 dated 02May 2003), here we study generalizations of infinitely divisible (ID) and max-infinitely divisible (MID) laws. We show that these generalizations appear as limits of random sums and random maximums respectively. For the random sample size N, we identify a class of probability generating functions. Necessary and sufficient conditions that implies the convergence to an ID (MID) law by the convergence to these generalizations and vise versa are given. The results generalize those on ID and random ID laws studied previously in Satheesh (2001b, 2002) and those on geometric MID laws studies in Rachev and Resnick (1991). We discuss attraction and partial attraction in this generalization of ID and MID laws.Comment: 14 pages, in journal format. In the first sentence of the last paragraph on page 131 the part after the second comma was inadvertently omitted and was missed even in the proof reading. This has been correcte

An Autoregressive Model with Semi-stable Marginals

The family of semi-stable laws is shown to be semi-selfdecomposable. Thus they qualify to model stationary first order autoregressive schemes. A connection between these autoregressive schemes with semi-stable marginals and semi-selfsimilar processes is given.Comment: PDF File, 5 Pages, corrections incorporated and contents change

A generalization of random self-decomposability

The notion of random self-decomposability is generalized here. Its relation to self-decomposability, Harris infinite divisibility and its connection with a stationary first order generalized autoregressive model are presented. The notion is then extended to $\mathbf{Z_+}$-valued distributions.Comment: 7 page

A Max-AR(1) Model with Max-Semistable Marginals

The structure of stationary first order max-autoregressive schemes with max-semi-stable marginals is studied. A connection between semi-selfsimilar extremal processes and this max-autoregressive scheme is discussed resulting in their characterizations. Corresponding cases of max-stable and selfsimilar extremal processes are also discussed.Comment: In journal format, 5 Pages, contents change

On the Marginal Distributions of Stationary AR(1) Sequences

In this note we correct an omission in our paper (Satheesh and Sandhya, 2005) in defining semi-selfdecomposable laws and also show with examples that the marginal distributions of a stationary AR(1) process need not even be infinitely divisible.Comment: 4 pages, in .pdf format, submitte

On Geometric Infinite Divisibility

The notion of geometric version of an infinitely divisible law is introduced. Concepts parallel to attraction and partial attraction are developed and studied in the setup of geometric summing of random variables.Comment: 7 page

A Generalization and Extension of an Autoregressive Model

Generalizations and extensions of a first order autoregressive model of Lawrance and Lewis (1981) are considered and characterized here.Comment: 10 pages, in .pdf format, submitte

Harris Family of Discrete Distributions

In this paper we discuss the basic properties of a discrete distribution introduced by Harris in 1948 and obtain a characterization of it. The divisibility properties of the distribution are also studied. We derive the moment and maximum likelihood estimators for both the parameters and verify them by simulated observations.Comment: 18 pages, submitte

A Generalization of the Marshal-Olkin Scheme and Related Processes

A generalization of the Marshal-Olkin parametrization scheme is developed and stochastic models related to it are discussed here.Comment: 6 pages, Presented at the National Conference on "Statistics for the Twenty First Century" organised by the Department of Statistics, University of Kerala, Trivandrum, India, 17-19 March 201