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Full Screen- TITLE
- CERTIFICATE
- DECLARATION
- ACKNOWLEDGEMENT
- CONTENTS
- 1 INTRODUCTION AND SUMMARY
- 1.1 Review of Literature
- 1.2 Summary of the Present Study
- 1.3 Preliminaries
- 1.3.1 Beta Distributions
- 1.3.2 Dirichlet Distributions
- 1.3.3 Jacobians of Matrix Transformations
- 1.3.4 Jacobians of Matrix Transformations in the Complex Case
- 1.3.5 Matrix-variate Beta Densities
- 1.3.6 Matrix-variate Dirichlet Densities
- 1.3.7 G-function
- 1.3.8 Whittaker Function
- 1.3.9 Bayesian Inference
- 1.3.10 Autoregressive Models
- 2 AN EXTENSION OF THE DIRICHLET DENSITY
- 2.1 Generalization of the Type-1 Dirichlet Density
- 2.2 Properties
- 2.3 An Application in Bayesian Analysis
- 2.3.1 Joint Posterior Moments
- 2.3.2 The Posterior Moments of p1 +....+ pk
- 2.3.3 An Application to Flood Data
- 2.4 Other Extensions of the New Model
- 3 EXTENSIONS OF THE MATRIX-VARIATE DIRICHLET DISTRIBUTIONS
- 3.1 A Generalized Real Inverted Dirichlet Model
- 3.2 An Extension of the Dirichlet Model in the Complex Case
- 4 GENERALIZED LAPLACIAN DISTRIBUTION AND SOME APPLICATIONS
- 4.1 The Generalized Laplacian Distribution
- 4.2 The Generalized Laplacian AR (1) Process
- 4.2.1 Distribution of sums and bivariate distribution of (Xn, Xn+1)
- 4.2.2 Simulation Studies
- 4.3 Probabilistic Design of Mechanical Systems Using Generalized Laplacian Distribution
- 4.3.1 Stress Strength Interference Theory with Gamma Distributed Stress and Strength
- 4.3.2 Density for a Gamma Difference
- 4.3.3 Reliability of Mechanical Systems
- References
- REFERENCES