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Full Screen- Title
- CERTIFICATE
- DECLARATION
- ACKNOWLEDGEMENT
- DEDICATION
- CONTENTS
- 1 Introduction and study
- 1.1 Non-Gaussian time series modeling-a review
- 1.2 Summary of the present study
- 1.3 Preliminary concepts
- 1.3.1 Infinite divisibility
- 1.3.2 Self decomposability
- 1.3.3 Stable distributions on R
- 1.3.4 Geometric Infinite divisibility
- Theorem 1.3.1
- Theorem 1.3.2
- Theorem 1.3.3 (Aalogue of Levy-Khintchine representation)
- Theorem 1.3.4 (Analogue of Levy-Khinchin representation)
- Theorem I.3.5 (Analogue of Kolmogorovs representation)
- 1.3.5 Bernstien function
- Theorem 1.3.6
- 1.3.6 Geometric stable distributions
- Definition
- Parameterizations of geometric stable laws
- Spcial cases
- 1 Strictly GS laws
- 2 Linnik distribution
- 3 Symmetric Linnik distribution
- 1.3.7 Geometrically strictly stable distributions
- 1.3.8 Mittag-Leffler distribution
- 1.3.9 α- Laplace distribution
- 1.3.10 Geometric exponential distribution
- 1.3.11 Generalized laplacian distribution
- 1.3.12 Stationary rime series
- 1.3.13 Time reversibility
- 1.3.14 Autoregressive models
- 2 Geometrical exponential distribution and applications
- 2.1 Introduction
- 2.2 Geometric exponential distribution
- Definition 2.2.1
- Remark 2.2.1
- Remark 2.2.2
- Theorem 2.2.1
- 2.3 Geometric gamma distribution
- Theorem 2.3.1
- Remark 2.3.1
- 2.4 Application of GED (λ) and GGD (λ, k) distributions in first order autoregressive time series modeling
- 2.4.1 The distribution of sums of stationary intervals
- 2.5 Generalization to a kth order autoregressive process
- 2.6 Geometric exponential distribution and subordinated process
- Definition 2.6.1
- Theorem 2.6.1
- 2.7 Graphs of density function and cumulative distribution function
- 3 Geometric Mittag-Leffler distribution and processes
- 3.1 Introduction
- 3.2 Geometric Mittag-Leffler distributions
- Definition 3.2.1
- Definition 3.2.2
- Theorem 3.2.1
- 3.3 Geornetrir semi Mittag-Leffler distributions
- Definition 3.3.1
- 3.4 Autoregressive models in geometric Mittag-Leffler marginals
- Definition 3.4.1
- Theorem 3.4.1
- 3.5 Joint distributions for (Xn, Xn-1)
- 3.6 Sum of stationary intervals
- Remark 3.6.1
- 3.7 Characterization of geometric Mittag-Leffler distribution
- Theorem 3.7.1
- 3.8 Generalisation to a kth order autoregressive process
- 3.9 Applications
- 4 Geometric α-laplace distribution and applications
- 4.1 Introduction
- 4.2 Semi α-Laplace distribution
- 4.3 Geometric semi α-Laplace distribution
- Definition 4.3.1
- Definition 4.3.2
- Theorem 1.3.1
- 4.4 AR (1) model with geometric semi α-Laplace marginals
- Theorem 3.4.1
- 4.4.1 The Joint distribution of (Xn, xn-1)
- 4.5 Geometric α-Laplace distribution
- Definition 4.5.1
- Definition 4.5.2
- Theorem 4.5.1
- Theorem 4.5.2
- 4.5.1 The Joint distribution of Xn and Xn-1
- 4.6 Geometric Laplace distribution
- Definition 4.6.1
- Definition 4.6.2
- Theorem 4.6.1
- Theorem 4.6.2
- 4.6.1 The joint distribution for (Xn, Xn-1)
- 4.7 Generalization to a kth order autoregressive process
- 4.8 Applications
- 5 Autoregressive processes with tailed marginals
- 5.1 Introduction
- 5.2 Exponential tailed distributions
- Result 5.2.1
- 5.3 Geometric exponential tailed distribution
- 5.4 Geometric gamma tailed distribution
- 5.5 Geometric Mittag - Leffler tailed distribution
- 5.6 Geometric semi Mittag-Leffler tailed distribution
- 5.7 Geometric semi α-Laplace tailed distribution
- Definition 5.7.1
- Definition 5.7.2
- Definition 5.7.3
- 5.8 Autoregressive models with tailed marginal distributions
- 5.8.1 Geometric exponential tailed autoregressive processes
- 5.8.2 Geometric gamma tailed autoregressive process
- Theorem 5.8.1
- 5.8.3. Geometric Mittag-Leffler tailed process
- Theorem 5.8.2
- 5.8.4. Geometric semi α-Laplace tailed first order autoregressive process
- Theorem 5.8.3
- References