




S. No. 
Chapter 
Title of the
Chapters 
Page 
Size (KB)






1 
0 
CONTENTS

ix 
22 KB 





2 
1 
INTRODUCTION
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

1 
33 KB 





3 
2 
LITERATURE REVIEW 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

4 
56 KB 





4 
3 
PROBABILITY FUNCTIONS CLOSED UNDER INVERSION
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)

12 
58 KB 





5 
4 
DIFFERENTIAL EQUATIONS FOR GENERATING SCUI DISTRIBUTIONS
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

20 
62 KB 





6 
5 
CHARACTERIZATIONS OF SOME SCUI DENSITY FUNCTIONS
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

27 
41 KB 





7 
6 
A NEWSCUI DENSITY
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

32 
95 KB 





8 
7 
SOME PROPERTIES OF THE CLASS OF SCUI DISTRIBUTIONS
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

43 
102 KB 





9 
8 
CUI DISTRIBUTIONS AND THEIR PROPERTIES
8.1
Introduction
8.2 Ratio of Analogous Distributions Method for Generating CUI
Distributions
8.3 Properties of Two–Parameter CUI Distributions

56 
141 KB 





10 
9 
REFERENCES 
73 
34 KB 




