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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