Truncated and censored samples: theory and applications
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Dekker
1991
|
| Edition: | 1. print. |
| Series: | Statistics
119 |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015371601&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Physical Description: | XIV, 312 S. graph. Darst. |
| ISBN: | 0824784472 |
Staff View
MARC
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| 245 | 1 | 0 | |a Truncated and censored samples |b theory and applications |
| 250 | |a 1. print. | ||
| 264 | 1 | |a New York [u.a.] |b Dekker |c 1991 | |
| 300 | |a XIV, 312 S. |b graph. Darst. | ||
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| adam_text | Contents
PREFACE v
LIST OF ILLUSTRATIONS xi
LIST OF TABLES xiii
1. INTRODUCTION 1
1.1 Preliminary Considerations 1
1.2 A Historical Account 2
1.3 Sample Types 3
1.4 Estimators 5
1.5 Likelihood Functions 6
2. SINGLY TRUNCATED AND SINGLY CENSORED SAMPLES
FROM THE NORMAL DISTRIBUTION 8
2.1 Preliminary Remarks 8
2.2 Some Fundamentals 8
2.3 Moment Estimators for Singly Truncated Samples 10
2.4 Three Moment Estimators for Singly Truncated Normal
Distribution Parameters 13
vii
viii Contents
2.5 Maximum Likelihood Estimators for Singly Censored
Samples 18
2.6 Sampling Errors of Estimates 25
2.7 Illustrative Examples 26
3. MULTIRESTRICTED SAMPLES FROM THE NORMAL
DISTRIBUTION 31
3.1 Introduction 31
3.2 Doubly Truncated Samples 31
3.3 Doubly Censored Samples 46
3.4 Progressively Censored Samples 50
3.5 Some Additional Sample Types 59
3.6 Final Comment 65
4. LINEAR ESTIMATORS 66
4.1 Introduction 66
4.2 Calculation of Estimates 67
4.3 Derivations 67
4.4 Alternative Estimators 70
4.5 Illustrative Examples 81
5. TRUNCATED AND CENSORED SAMPLES FROM THE
WEIBULL DISTRIBUTION 85
5.1 Introduction 85
5.2 Distribution Characteristics 85
5.3 Singly Censored Samples 86
5.4 Progressively Censored Samples 88
5.5 The Three Parameter Distribution 90
5.6 Modified Maximum Likelihood Estimators (MMLE) 92
5.7 Errors of Estimates 93
5.8 An Illustrative Example 94
6. TRUNCATED AND CENSORED SAMPLES FROM
THE LOGNORMAL DISTRIBUTION 96
6.1 Introduction 96
6.2 Some Fundamentals 96
6.3 Global Maximum Likelihood Estimation 97
6.4 Local Maximum Likelihood and Modified Maximum
Likelihood Estimators for Censored Samples 98
6.5 Computational Procedures 101
Contents ix
6.6 Errors of Estimates 104
6.7 An Illustrative Example 104
7. TRUNCATED AND CENSORED SAMPLES FROM THE
INVERSE GAUSSIAN AND THE GAMMA DISTRIBUTIONS 106
7.1 The Inverse Gaussian Distribution 106
7.2 The Gamma Distribution 113
7.3 A Pseudo Complete Sample Technique for Parameter
Estimation from Censored Samples 121
7.4 An Illustrative Example 123
8. TRUNCATED AND CENSORED SAMPLES FROM
THE EXPONENTIAL AND THE EXTREME VALUE
DISTRIBUTIONS 128
8.1 The Exponential Distribution 128
8.2 The Extreme Value Distribution 139
9. TRUNCATED AND CENSORED SAMPLES FROM THE
RAYLEIGH DISTRIBUTION 146
9.1 Introduction 146
9.2 Some Special Cases 147
9.3 Parameter Estimation 151
9.4 Reliability of Estimates 156
9.5 Illustrative Examples 159
9.6 Some Concluding Remarks 164
10. TRUNCATED AND CENSORED SAMPLES FROM THE
PARETO DISTRIBUTION 165
10.1 Introduction 165
10.2 Some Fundamentals 165
10.3 Parameter Estimation 168
10.4 Estimate Reliability 171
10.5 An Illustrative Example 172
11. HIGHER MOMENT ESTIMATES OF PEARSON
DISTRIBUTION PARAMETERS FROM
TRUNCATED SAMPLES 174
11.1 Introduction 174
11.2 The Pearson Distributions 174
x Contents
11.3 Recursion Formula for Moments of a Truncated
Distribution 177
11.4 Parameter Estimation from Doubly Truncated Samples 178
11.5 Determining the Distribution Type 180
11.6 Singly Truncated Samples 180
11.7 Type III and Normal Distributions 181
11.8 A Numerical Example 182
12. TRUNCATED AND CENSORED SAMPLES FROM
BIVARIATE AND MULTIVARIATE NORMAL
DISTRIBUTIONS 185
12.1 Introduction 185
12.2 Estimation in the Bivariate Normal Distribution 186
12.3 Reliability of Estimates 190
12.4 An Illustrative Example 191
12.5 Parameter Estimation in the Multivariate Normal
Distribution 193
13. TRUNCATED AND CENSORED SAMPLES FROM
DISCRETE DISTRIBUTIONS 199
13.1 Introduction 199
13.2 The Poisson Distribution 199
13.3 The Negative Binomial Distribution 208
13.4 The Binomial Distribution 212
13.5 The Hypergeometric Distribution 215
14. TRUNCATED ATTRIBUTE SAMPLING AND RELATED
TOPICS 220
14.1 Truncated Attribute Acceptance Sampling 220
14.2 Estimation from Misclassified Inspection Data 224
14.3 Inflated Zero Distributions 236
APPENDIX: TABLES OF CUMULATIVE STANDARD
DISTRIBUTION FUNCTIONS 245
GLOSSARY 279
BIBLIOGRAPHY 289
INDEX 305
List of Illustrations
2.1 Graph of Auxiliary Estimation Function 6(a) for Singly
Truncated Samples from the Normal Distribution 14
2.2 Efficiency Curves of Three Moment Estimates from Singly
Truncated Samples from the Normal Distribution 18
3.1 Graphs of Estimating Functions for Doubly Truncated Samples
from the Normal Distribution 42
3.2 Probit Regression Line 60
5.1 The Weibull Coefficient of Variation and Its Square as
Functions of the Shape Parameter 89
7.1 Graphs of a( as a Function of zx and n in Complete Samples
from the Inverse Gaussian Distribution 124
7.2 Graphs of a3 as a Function of z, and n in Complete Samples
from the Gamma Distribution 125
8.1 Probability Density Function of the Exponential Distribution 130
8.2 Cumulative Probability Function of the Exponential Distribution 131
8.3 A Cumulative Hazard Plot of Generator Fan Data 138
xi
xii List of Illustrations
8.4 Probability Density Functions of Extreme Value Distributions 142
9.1 Graphs of Estimating Functions for Truncated Samples from
Two and Three Dimensional Rayleigh Distributions 159
10.1 Probability Density Function of the Pareto Distribution: a = 4.1 167
10.2 Cumulative Probability Function of the Pareto Distribution:
a = 4.1 168
11.1 Pi (32 Curves for the Pearson System of Distribution Functions 179
List of Tables
2.1 Auxiliary Estimation Function 6(a) for Singly Truncated
Samples from the Normal Distribution 12
2.2 Asymptotic Variances and Efficiencies of Three Moment
Estimates from Singly Truncated Samples from the Normal
Distribution 17
2.3 Auxiliary Estimation Function (h, a) for Singly Censored
Samples from the Normal Distribution 21
2.4 Variance and Covariance Factors for Singly Truncated and
Singly Censored Samples from the Normal Distribution 27
3.1 Estimating Functions Ht (£;,, £2) and Hi (4i ki) for Doubly
Truncated Samples from the Normal Distribution 34
3.2 The Functions Q, i^Q, Q , X, r for Progressively Censored
Samples from the Normal Distribution 52
3.3 Life Distribution of Certain Biological Specimens in a
Stress Environment 58
4.1 Coefficients of Linear Estimates of the Mean and Standard
Deviation for Censored Samples from the Normal Distribution 72
xiii
xiv List of Tables
4.2 Variances and Covariances of Linear Estimates of the Mean
and Standard Deviation for Censored Samples from the
Normal Distribution 80
4.3 Variances and Relative Efficiencies of Gupta s Alternative
Linear Estimates of the Mean and Standard Deviation
for Censored Samples from the Normal Distribution 83
6.1 Expected Values of the First Order Statistic in Samples
from the Standard Normal Distribution 101
7.1 A Random Sample from an Inverse Gaussian Distribution 126
7.2 Summary of Estimates of Inverse Gaussian Parameters 126
7.3 Successive Iterations of Censored Observations for
Pseudo Complete Samples from the Inverse Gaussian
Distribution 127
8.1 A Progressively Censored Sample Consisting of Life Span
Observations of 70 Generator Fans 137
9.1 Truncated Sample Estimating Function J2(z) for Rayleigh
Distribution 157
9.2 Truncated Sample Estimating Function J3(z) for Rayleigh
Distribution 158
9.3 Censored Sample Estimation Function H3(h,z) for Rayleigh
Distribution 160
10.1 Some Characteristics of the Pareto Distribution 169
11.1 Weight Distribution of 1000 Women Students 183
12.1 Summary of Estimates and Their Variances for Example 12.1 193
12.2 Summary of Sample Data for Example 12.2 195
12.3 Summary of Estimates for Example 12.2 196
14.1 Characteristics of Curtailed Sampling Plans 225
A.I Cumulative Distribution Function of the Standardized Weibull
Distribution 246
A.2 Cumulative Distribution Function of the Standardized
Lognormal Distribution 254
A.3 Cumulative Distribution Function of the Standardized Inverse
Gaussian Distribution 262
A.4 Cumulative Distribution Function of the Standardized
Gamma Distribution 270
|
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| discipline | Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV022156939 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T12:49:10Z |
| institution | BVB |
| isbn | 0824784472 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015371601 |
| oclc_num | 23383180 |
| open_access_boolean | |
| owner | DE-706 |
| owner_facet | DE-706 |
| physical | XIV, 312 S. graph. Darst. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Dekker |
| record_format | marc |
| series | Statistics |
| series2 | Statistics |
| spellingShingle | Cohen, Alonzo Clifford 1911-2000 Truncated and censored samples theory and applications Statistics Echantillonnage (Statistique) ram Estimation, Théorie de l' Estimation, théorie de l' ram Échantillonnage (Statistique) Estimation theory Sampling (Statistics) Zensierte Stichprobe (DE-588)4292948-9 gnd Gestutzte Stichprobe (DE-588)4292947-7 gnd Schätztheorie (DE-588)4121608-8 gnd Stichprobe (DE-588)4057502-0 gnd Datenerhebung (DE-588)4155272-6 gnd |
| subject_GND | (DE-588)4292948-9 (DE-588)4292947-7 (DE-588)4121608-8 (DE-588)4057502-0 (DE-588)4155272-6 |
| title | Truncated and censored samples theory and applications |
| title_auth | Truncated and censored samples theory and applications |
| title_exact_search | Truncated and censored samples theory and applications |
| title_full | Truncated and censored samples theory and applications |
| title_fullStr | Truncated and censored samples theory and applications |
| title_full_unstemmed | Truncated and censored samples theory and applications |
| title_short | Truncated and censored samples |
| title_sort | truncated and censored samples theory and applications |
| title_sub | theory and applications |
| topic | Echantillonnage (Statistique) ram Estimation, Théorie de l' Estimation, théorie de l' ram Échantillonnage (Statistique) Estimation theory Sampling (Statistics) Zensierte Stichprobe (DE-588)4292948-9 gnd Gestutzte Stichprobe (DE-588)4292947-7 gnd Schätztheorie (DE-588)4121608-8 gnd Stichprobe (DE-588)4057502-0 gnd Datenerhebung (DE-588)4155272-6 gnd |
| topic_facet | Echantillonnage (Statistique) Estimation, Théorie de l' Estimation, théorie de l' Échantillonnage (Statistique) Estimation theory Sampling (Statistics) Zensierte Stichprobe Gestutzte Stichprobe Schätztheorie Stichprobe Datenerhebung |
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| volume_link | (DE-604)BV000003265 |
| work_keys_str_mv | AT cohenalonzoclifford truncatedandcensoredsamplestheoryandapplications |