A further generalization of random self-decomposability
The notion of random self-decomposability is generalized further. The notion is then extended to non-negative integer-valued distributions.
math.PR↗
arXiv subjects
E Sandhya
Publications and source records attributed to E Sandhya.
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.
math.PR↗
Non-Negative Integer-Valued Semi-Selfsimilar Processes
Non-negative integer-valued semi-selfsimilar processes are introduced. Levy processes in this class are characterized. Its relation to an AR(1) scheme is derived.
math.PR↗
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.
math.PR↗
A Generalization of Stationary AR(1) Schemes
Here we develop a first order autoregressive model {Xn} that is marginally stationary where Xn is the sum/ extreme of k i.i.d observations. We prove that stationary solutions to these models are either semi-selfdecomposable/ extreme-semi-selfdecomposable or, sum/ extreme stable with respect to Harris distribution.
math.PR↗
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.
math.PR↗
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.
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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.
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Semi-Selfdecomposable Laws and Related Processes
In this note we identify the class of distributions for {Xn} that can generate a linear, additive, first order auto-regressive scheme that is marginally stationary as semi-selfdecomposable laws. We give a method to construct these distributions. Its implications in subordination and selfdecomposability of Levy processes are given. The discrete analogues of these processes are also discussed.
math.PR↗
Max-Semi-Selfdecomposable Laws and Related Processes
Methods of construction of Max-semi-selfdecompsable laws are given. Implications of this method in random time changed extremal processes are discussed. Max-autoregressive model is introduced and characterized using the max-semi-selfdecompsable laws and exponential max-semi-stable laws. Max-semi-selfddecomposability of max-semi-stable laws are proved.
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Semi-Selfdecomposable Laws in the Minimum Scheme
We discuss semi-selfdecomposable laws in the minimum scheme and characterize them using an autoregressive model. Semi-Pareto and semi-Weibull laws of Pillai (1991) are shown to be semi-selfdecomposable in this scheme. Methods for deriving this class of laws are then attempted from the angle of randomization. Finally, discrete analogues of these results are also considered.
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Characterizations of the Extended Geometric, Harris, Negative Binomial and Gamma Distributions
Extended geometric distribution is defined and its mixture is characterized by the property of having completely monotone probability sequence. Also, convolution equations and probability generating functions are used to characterize extended geometric distributions. Further, some characterizations of Harris and negative binomial distributions based on probability generating functions are obtained. Relations between these distributions are derived and finally a gamma distribution is characterized in terms of its Laplace transform.
math.ST↗
Harris Processes
In this paper, we develop two stochastic models where the variable under consideration follows Harris distribution. The mean and variance of the processes are derived and the processes are shown to be non-stationary. In the second model, starting with a Poisson process, an alternate way of obtaining Harris process is introduced.
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