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TITLE
CERTIFICATE
DECLARATION
ACKNOWLEDGEMENT
CONTENTS
1. INTRODUCTION
1.1 Introduction and Review of the Literature
1.2 Summary of the Present Work
2. LOG-SYMMETRIC DISTRIBUTIONS
2.1 Introduction
2.2 Definition and Properties
2.2.1 Properties
2.3 Some Examples of Log-Symmetric Distributions.
2.3.1 A Mixture of Pareto and Power Distributions
2.3.2 Lognormal Distribution
2.3.3 Log-Laplace Distribution
2.3.4 Loglogistic Distribution
2.3.5 Cauchy Distribution
2.4 Stable Distribution
3. A CLASS OF DOUBLE LOG-SYMMETRIC DISTRIBUTIONS
3.1 Introduction
3.2 Class of Distributions
3.2.1 Table of Distribution Functions
3.3 Some Properties
3.3.1 A Characterization of Cauchy Distribution
3.4 Generation Algorithm
3.4.1 Acceptance-Rejection Method
3.4.2 Acceptance-Compliment Method
3.5 Some Related Works
4. ESTIMATION OF PARAMETERS OF DOUBLE LOG-SYMMETRIC DISTRIBUTIONS
4.1 Introduction
4.2 Estimation of Location Parameter Using Quasi - mid range
4.3 Estimation of Scale Parameter Using Quasi - range
4.4 Numerical Illustrations
4.5 Window Estimator for Index Parameter p of the Generalized Cauchy Distribution
4.5.1 Method of Estimation
4.5.2 Results of a Simulation Experiment
5. LOGSYMMETRIC DISTRIBUTIONS AND UNDER-REPORTING
5.1 Introduction
5.2 Case 1: Actual Variable Follows Log-Laplace distribution
5.3 Estimation of Parameters
5.4 Case 2: Actual Variable Follows Modified Form of log-Laplace distribution
5.5 Maximum Likelihood Estimation
5.6 A Case Study
APPENDIX
APPENDIX A1 Programme for Estimating Location Parameter and Scale parameter using Quasi Mid-range and Quasi-range
APPENDIX A2 Programme for estimating p of generalized Cauchy distribution v z window estimate
APPENDIX A3 Programme for estimating p of generalized Cauchy distribution viz window estimate (Acceptance Rejection Method)
APPENDIX A4 Programmes for density plot using mathstatica package
REFERENCES