Title of Thesis

On A Class Of Distributions Closed Under Inversion

Author(s)

Saleha Naghmi Habibullah

Abstract
Not Available

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1.1 Preliminary Remarks
1.2 Inverted and Inverse Distributions
1.3 The Class of Inverted Distributions
1.4 Closure and Strict Closure Under Inversion
1.5 Research Objectives

2.1 Introduction
2.2 Inverted Distributions
2.3 Inverse Moments
2.4 Closure and Strict Closure Under Inversion
2.5 Differential Equations for Generating Systems of Distributions

3.1 Introduction
3.2 Main Results by Gumbel and Keeney (1950)
3.3 Main Results by Seshadri (1965)
3.4 Main Results by Saunders (1974)

4.1 Introduction
4.2 A Differential Equation for Generating SCUI Distributions
4.3 Examples
4.4 An Additional Differential Equation for Generating SCUI Distributions
4.5 Examples

5.1 Introduction
5.2 Characterization of the Log Pearson Type VII Distribution
5.3 Characterization of Seshadri (1965)’s Distribution (n) with r = 0

6.1 Introduction
6.2 Differential Equation for the Case a < x <1/ a,0 < a <1
6.3 An SCUI Density Defined on (a,1/ a), 0 < a <1

7.1 Introduction
7.2 Properties Pertaining to Mathematical Expectation
7.3 Properties Pertaining to Truncation
7.4 Properties Pertaining to Order Statistics
7.5 Linear Combinations of SCUI Density Functions
7.6 Products of Random Variables with SCUI Density Functions
7.7 Likelihood Function of A Random Sample from an SCUI Density Function
7.8 Functional Form of An SCUI Density Function

8.1 Introduction
8.2 Ratio of Analogous Distributions Method for Generating CUI Distributions
8.3 Properties of Two–Parameter CUI Distributions

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