Normal and Student ́s t Distributions and Their Applications

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Springer Science & Business Media, Feb 7, 2014 - Mathematics - 157 pages
The most important properties of normal and Student t-distributions are presented. A number of applications of these properties are demonstrated. New related results dealing with the distributions of the sum, product and ratio of the independent normal and Student distributions are presented. The materials will be useful to the advanced undergraduate and graduate students and practitioners in the various fields of science and engineering.
 

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Contents

1 Introduction
1
2 Normal Distribution
7
3 Students t Distribution
51
4 Sum Product and Ratio for the Normal Random Variables
63
5 Sum Product and Ratio for the Students t Random Variables
80
6 Sum Product and Ratio for the Normal and Students t Random Variables
93
7 Product of the Normal and Students t Densities
102
8 Characterizations of Normal Distribution
113
9 Characterizations of Students t Distribution
128
10 Concluding Remarks and Some Future Research
143
References
145
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