I= NEGATIVE AND FACTORIAL MOMENTS OF DISCRETE DISTRIBUTIONS INVOLVING HYPER-GEOMETRIC SERIES FUNCTIONS
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Title of Thesis
NEGATIVE AND FACTORIAL MOMENTS OF DISCRETE DISTRIBUTIONS INVOLVING HYPER-GEOMETRIC SERIES FUNCTIONS

Author(s)
Ayesha Roohi
Institute/University/Department Details
National College of Business Administration & Economics
Session
December, 2003
Subject
Statistics
Number of Pages
117
Keywords (Extracted from title, table of contents and abstract of thesis)
negative moments, negative factorial, hyper-geometric series functions

Abstract
Early authors gave approximate results for negative moments of certain discrete distributions truncated at zero. Chao and Strawderman (1972) gave a technique of obtaining negative moments of the form E [(X+A)-k], Lepage (1978) and Jones (1987) discussed negative factorial moments.

In this dissertation, negative moments and negative factorial moments of generalized hyper-geometric series distributions have been investigated, with special reference to the binomial, hyper-Poisson, Poisson, negative binomial, geometric and logarithmic series distributions. These moments have been expressed in terms of hyper-geometric series functions. Recurrence relations for the negative moments and negative factorial moments of some discrete distributions have been derived using properties of hyper-geometric series functions. Further characterizations of some discrete distributions have been discussed using properties of negative moments.

New properties regarding sums and integrals of hyper-geometric functions have also been derived, using properties of probability distributions. Certain limiting cases of hyper- geometric functions have also been discussed.
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725.04 KB
S. No. Chapter Title of the Chapters Page Size (KB)
1 0 Contents
47.81 KB
2 1 Introduction 1
53.32 KB
3 2 Negative Moments and Negative Factorial Moments 7
64.26 KB
  2.1 Introduction 7
  2.2 First Order Negative Moments 7
  2.3 Negative Factorial Moments 10
  2.4 Relation between the Mean of a Zero Truncated Distribution and its First Order Negative Moment 13
4 3 Representation of Negative Moments of Some Discrete Distribution in Terms of Hyper- Geometric Series Functions 15
121.59 KB
  3.1 Introduction 15
  3.2 Negative moments 18
  3.3 Negative factorial moments 26
5 4 Recurrence Relations of Negative Moments 33
121.73 KB
  4.1 Introduction 33
6 5 Negative Moments of generalized hyper- Geometric series distribution 51
125.85 KB
  5.1 Introduction 51
  5.2 A subclass of modified power series Distributions 61
7 6 Negative Moment Estimation 68
68.44 KB
  6.1 Introduction 68
  6.2 Estimation 68
  6.3 Asymptotic variance of negative moment Estimators 72
8 7 Properties of Hyper-geometric Series Functions Using Probability Distributions 77
167.88 KB
  7.1 Introduction 77
  7.2 Properties 77
9 8 Characterizations of Some Distributions Using Recurrence Relations for Negative Moments 102
63.62 KB
10 9 References 112
52.18 KB