Environmental Statistics: Methods and Applications (Wiley Series in Probability and Statistics)

317 Pages·2004·12.14 MB·English

by  Vic Barnett

Environmental Statistics
WILEYSERIES INPROBABILITYAND STATISTICS
Established by WALTERA. SHEWHART and SAMUEL S. WILKS
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Editors Emeriti: Vic Barnett,J. Stuart Hunter, DavidG. Kendall
Acomplete listof the titles in this series appears atthe end of this volume.
Environmental Statistics
Methods and Applications
VIC BARNETT
NottinghamTrentUniversity,UK
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Contents
Preface xiii
Chapter 1 Introduction 1
1.1 Tomorrow istoo Late! 2
1.2 EnvironmentalStatistics 2
1.3 SomeExamples 5
1.3.1 ‘Gettingit all together’ 5
1.3.2 ‘Intimeandspace’ 8
1.3.3 ‘Keep it simple’ 10
1.3.4 ‘How much can we take?’ 12
1.3.5 ‘Over the top’ 14
1.4 Fundamentals 16
1.5 Bibliography 18
PART I EXTREMAL STRESSES: EXTREMES,OUTLIERS,ROBUSTNESS 21
Chapter 2 Ordering and Extremes: Applications, models,inference 23
2.1 Ordering theSample 24
2.1.1 Order statistics 25
2.2 Order-based Inference 26
2.3 Extremes and ExtremalProcesses 32
2.3.1 Practicalstudy and empirical models;generalized
extreme-value distributions 37
2.4 Peaks overThresholds and theGeneralized
ParetoDistribution 40
Chapter 3 Outliers and Robustness 45
3.1 Whatisan Outlier? 45
3.2 Outlier Aims and Objectives 46
3.3 Outlier-Generating Models 49
3.3.1 Discordancy and models for outlier generation 49
3.3.2 Tests of discordancy for specific distributions 51
3.4 Multiple Outliers: Masking and Swamping 53
viii
CONTENTS
3.5 Accommodation:Outlier-RobustMethods 54
3.6 APossible New Approach to Outliers 55
3.7 MultivariateOutliers 56
3.8 Detecting MultivariateOutliers 58
3.8.1 Principles 59
3.8.2 Informalmethods 60
3.9 Tests of Discordancy 66
3.10 Accommodation 68
3.11 Outliersin linear models 70
3.12 Robustnessin General 72
PART II COLLECTINGENVIRONMENTALDATA:SAMPLING
ANDMONITORING 75
Chapter 4 Finite-Population Sampling 77
4.1 AProbabilisticSampling Scheme 78
4.2 Simple RandomSampling 79
4.2.1 Estimating the mean, X 81
4.2.2 Estimating the variance, S2 82
4.2.3 Choice ofsample size, n 84
4.2.4 Estimating the population total, XT 85
4.2.5 Estimating a proportion, P 86
4.3 Ratios and Ratio Estimators 89
4.3.1 The estimation of a ratio 90
4.3.2 Ratioestimator of apopulation total or mean 92
4.4 Stratified(simple) Random Sampling 96
4.4.1 Comparing thesimplerandomsample mean
and the stratified sample mean 99
4.4.2 Choice ofsample sizes 100
4.4.3 Comparison ofproportionalallocation and
optimum allocation 102
4.4.4 Optimum allocation for estimatingproportions 103
4.5 Developments of Survey Sampling 103
Chapter 5 Inaccessible and Sensitive Data 105
5.1 Encountered Data 106
5.2 Length-Biased or Size-Biased Sampling and
Weighted Distributions 107
5.2.1 Weighted distribution methods 108
5.3 Composite Sampling 112
5.3.1 Attribute Sampling 112
5.3.2 Continuous variables 115
5.3.3 Estimating mean and variance 115
ix
CONTENTS
5.4 Ranked-Set Sampling 117
5.4.1 The ranked-set sample mean 119
5.4.2 Optimal estimation 122
5.4.3 Ranked-set sampling fornormal and
exponential distributions 124
5.4.4 Imperfect ordering 126
Chapter 6 Sampling inthe Wild 131
6.1 Quadrat Sampling 131
6.2 Recapture Sampling 132
6.2.1 The Petersen and Chapman estimators 133
6.2.2 Capture–recapture methods inopen
populations 136
6.3 Transect Sampling 138
6.3.1 The simplest case: strip transects 139
6.3.2 Using a detectability function 142
6.3.3 Estimating f(y) 144
6.3.4 Modifications of approach 146
6.3.5 Point transects orvariable circular plots 147
6.4 Adaptive Sampling 148
6.4.1 Simple models foradaptive sampling 149
Part III EXAMININGENVIRONMENTALEFFECTS:
STIMULUS–RESPONSERELATIONSHIPS 151
Chapter 7 Relationship:regression-type models and methods 153
7.1 LinearModels 154
7.1.1 The linearmodel 156
7.1.2 The extended linear model 158
7.1.3 The normal linear model 160
7.2 Transformations 161
7.2.1 Lookingat the data 162
7.2.2 Simple transformations 166
7.2.3 Generaltransformations 168
7.3 The Generalized Linear Model 171
Chapter 8 Special Relationship Models, Including Quantal Response
andRepeated Measures 175
8.1 Toxicology Concerns 176
8.2 Quantal Response 178
8.3 Bioassay 180
8.4 Repeated Measures 182