2,826 research outputs found
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 -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
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