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Title
CERTIFICATE
DECLARATION
ACKNOWLEDGEMENT
CONTENTS
1. Preliminary Concepts and Summary
1.1 Introduction
1.2 Preliminaries
1.2.1 Stationary time series
1.2.2 Autoregressive models
1.2.3 Non-Gaussian time series model
1.3 Review of results and concepts
1.3.1 Adding a parameter to a family of distributions
1.3.2 Geometric infinite divisibility & geometric extreme stability
1.3.3 Semi-Weibull distributions
1.3.4 Semi-Pareto distributions
1.3.5 Semi-logistic distributions
1.3.6 Extreme value distributions
1.3.7 Domain of attraction
1.3.8 Some reliability concepts
1.3.8.1 Univariate case
1.3.8.2 Bivariate case
1.3.8.3 Bivariate failure rate
1.4 Summary of the present study
2. Marshall-Olkin Exponential Distribution & Applications
2.1 Introduction
2.2 Marshall-Olkin exponential family of distributions
2.3 An AR (1) model with MO-GE marginal distribution
2.4 Sample path behaviour
2.5 Generalization to the kth order autoregressive model
2.6 Generation of MO-GEAR (1) process
3. Marshall-Olkin Semi-Weibull Distributions & Processes
3.1 Introduction
3.2 Marshall-Olkin semi-Weibull distribution and properties
3.3 An AR (1) model with MO-SW marginal distributions
3.4 Marshall-Olkin generalized Weibull distribution
3.5 An AR (1) model. with MO-GW marginal distribution
3.5.1 Sample path behaviour
3.6 Marshall-Olkin bivariate Weibull family of distributions
3.7 Marshall-Olkin bivariate semi-Weibull AR (1) model
3.8 Generalization to the kth order autoregressive model
4. Univariate And Bivariate Pareto Processes
4.1 Introduction
4.2 Marshall-Olkin semi-Pareto family
4.3 An AR (1) model with MO-SP marginal distribution
4.4 Marshall-Olkin Pareto distribution and its properties
4.4.1 Sample path behaviour
4.5 Estimation of parameters
4.5.1 Estimators from moments
4.5.2 Maximum likelihood estimators
4.5.3 Estimation from Quantiles
4.6 Marshall-Olkin bivariate semi-Pareto distributions
4.7 Marshall-Olkin bivariate semi-Pareto AR (1) model
4.8 Generalization to the kth order autoregressive model
4.9 Characterizations
5. Logistic Processes
5.1 Introduction
5.2 Marshall-Olkin generalized logistic family
5.3 An AR (1) model with MO-GL marginal distribution
5.3.1 Sample path behaviour
5.4 Semi-logistic family of distributions
5.5 An AR (I) model with MO-SL marginal distribution
5.6 Marshall-Olkin bivariate logistic family of distributions
6. Extreme Value Distributions and Processes
6.1 Introduction
6.2 Marshall-Olkin generalized Gumbel family
6.3 An AR (1) model with MO-GUMX marginal distribution
6.4 Marshall-Olkin Gumbel distribution for minimum
6.5 An AR (1) model with MO-GUMN marginal distribution
6.6 Marshall-Olkin Frechet distribution for maximum
6.7 An AR (1) model with MO-FRMX marginal distribution
6.8 Marshall-Olkin Frechet distribution for minimum
6.9 An AR (1) model with MO-FRMN marginal distribution
6.10 Marshall-Olkin Weibull distribution for maximum
6.11 Marshall-Olkin Weibull distribution for minimum
6.12 Important functions of some bivariate exponentials
7. Multivariate Generalizations
7.1 Introduction
7.2 Marshall-Olkin multivariate family of distributions
7.3 An AR (1) model with MO-MSP marginal distribution
7.4 A p-variate AR (k) model
8. Applications
8.1 Introduction
8.2 Reliability characteristics of MO-BP distribution
8.3 Applications to analysis of incomes
8.4 Reliability characteristics of MO-GE distribution
8.4.1 Derivation of the model
8.5 Case study
References