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E-grāmata: Inverse Gaussian Distribution: Theory: Methodology, and Applications [Taylor & Francis e-book]

(Indian Institute of Technology, Kanpur, India)
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Inverse Gaussian Distribution: Theory: Methodology, and ApplicationsPalielināt
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This monograph is a compilation of research on the inverse Gaussian distribution. It emphasizes the presentation of the statistical properties, methods, and applications of the two-parameter inverse Gaussian family of distribution. It is useful to statisticians and users of statistical distribution.
Preface iii
1 Introduction
1(6)
1.1 Background and Purpose of the Study
1(1)
1.2 Historical Review of the Inverse Gaussian Distribution
2(2)
1.3 Analogies with Normal Distribution Theory
4(1)
1.4 Applications of the Inverse Gaussian Distribution
4(1)
1.5 Problems of Data Analysis with Skewed Distributions
5(2)
2 Properties of the Inverse Gaussian Distribution
7(16)
2.1 Introduction
7(1)
2.2 Probability Density Function
7(4)
2.3 Characteristic Function and Moments
11(2)
2.4 Some Useful Properties
13(1)
2.5 Distribution Function
14(2)
2.6 Standardization of Inverse Gaussian
16(2)
2.7 A Three-Parameter Inverse Gaussian Distribution
18(2)
2.8 A Generalized Inverse Gaussian Distribution
20(3)
3 Genesis
23(16)
3.1 Introduction
23(1)
3.2 First Passage Time in a Wiener Process
23(7)
3.3 Wald's Distribution: Sample Size Distribution in a Sequential Probability Ratio Test
30(2)
3.4 Inversion Law: A Fundamental Characteristic of Inversely Related Variables
32(7)
4 Certain Useful Transformations and Characterizations
39(16)
4.1 Related Statistical Distributions
39(1)
4.2 Analogy with the Normal Distribution Theory
40(2)
4.3 Distribution of the Reciprocal of the Inverse Gaussian Variable
42(4)
4.4 Some Characterizations of the Inverse Gaussian Distribution
46(6)
4.5 Generating Random Variates from the Inverse Gaussian Distribution
52(3)
5 Sampling and Estimation of Parameters
55(20)
5.1 Maximum Likelihood Estimators
55(2)
5.2 Variance Estimation
57(3)
5.3 The Role of the Harmonic Mean
60(1)
5.4 Sampling Distributions
61(6)
5.5 Estimation for the Three-Parameter Distribution
67(4)
5.6 Goodness of Fit
71(1)
5.7 An Example
71(4)
6 Significance Tests
75(26)
6.1 Introduction
75(1)
6.2 One-Sample Methods
75(11)
6.3 Two-Sample Methods
86(6)
6.4 Analysis of Residuals
92(9)
7 Bayesian Inference
101(14)
7.1 On the Choice of a Prior Distribution
101(1)
7.2 The Parameterization (n, X)
101(4)
7.3 The Parameterization (l/ftA)
105(4)
7.4 Highest Probability Density (HPD) Regions
109(3)
7.5 Predictive Inference
112(2)
7.6 Additional Remarks
114(1)
8 Regression Analysis
115(16)
8.1 Introduction
115(1)
8.2 Simple Linear Regression Model: Zero Intercept
116(5)
8.3 Simple Linear Regression Model with Intercept
121(2)
8.4 Nonlinear Regression Models
123(8)
9 Life Testing and Reliability
131(28)
9.1 Introduction
131(1)
9.2 Estimation of Reliability Function
132(8)
9.3 Tolerance Limits
140(4)
9.4 Prediction Limits
144(6)
9.5 Failure Rate
150(4)
9.6 Mean Residual Life
154(2)
9.7 Inverse Gaussian Versus Other Distributions as Lifetime Models
156(3)
10 Applications
159(26)
10.1 Introduction
159(1)
10.2 Tracer Dynamics
160(5)
10.3 Emptiness of a Dam
165(2)
10.4 A Purchase Incidence Model
167(2)
10.5 The Distribution of Strike Duration
169(4)
10.6 A Word Frequency Distribution
173(4)
10.7 Other Applications
177(8)
11 Additional Topics
185(10)
11.1 Bivariate Inverse Gaussian Distributions
185(7)
11.2 Multivariate Inverse Gaussian Distributions
192(1)
11.3 An Inverse Gaussian Process
193(2)
Bibliography 195(14)
Index 209
Raj Chhikara is emeritus professor at UHCL.
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