Aims and Tools / Chapter 1: |
Aims / 1.0.: |
Conditions / 1.0.1.: |
History / 1.0.2.: |
The Flood Problem / 1.0.3.: |
Methodology / 1.0.4.: |
Arrangement of Contents / 1.0.5.: |
General Tools / 1.1.: |
Linear Transformations / 1.1.1.: |
Other Transformations / 1.1.2.: |
Symmetry / 1.1.3.: |
Measures of Dispersion / 1.1.4.: |
Moments / 1.1.5.: |
Generating Function / 1.1.6.: |
Convolution / 1.1.7.: |
The Gamma Function / 1.1.8.: |
The Logarithmic Normal Distribution / 1.1.9.: |
Specific Tools / 1.2.: |
Problems / 1.2.0.: |
The Intensity Function / 1.2.1.: |
The Distribution of Repeated Occurrences / 1.2.2.: |
Analysis of Return Periods / 1.2.3.: |
"Observed" Distributions / 1.2.4.: |
Construction of Probability Papers / 1.2.5.: |
The Plotting Problem / 1.2.6.: |
Conditions for Plotting Positions / 1.2.7.: |
Fitting Straight Lines on Probability Papers / 1.2.8.: |
Application to the Normal Distribution / 1.2.9.: |
Order Statistics and Their Exceedances / Chapter 2: |
Order Statistics / 2.1.: |
Distributions / 2.1.0.: |
Averages / 2.1.2.: |
Distribution of Frequencies / 2.1.3.: |
Asymptotic Distribution of mth Central Values / 2.1.4.: |
The Order Statistic with Minimum Variance / 2.1.5.: |
Control Band / 2.1.6.: |
Joint Distribution of Order Statistics / 2.1.7.: |
Distribution of Distances / 2.1.8.: |
The Distribution of Exceedances / 2.2.: |
Introduction / 2.2.0.: |
Distribution of the Number of Exceedances / 2.2.1.: |
The Median / 2.2.2.: |
The Probability of Exceedances as Tolerance Limit / 2.2.4.: |
Extrapolation from Small Samples / 2.2.5.: |
Normal and Rare Exceedances / 2.2.6.: |
Frequent Exceedances / 2.2.7.: |
Summary / 2.2.8.: |
Exact Distribution of Extremes / Chapter 3: |
Averages of Extremes / 3.1.: |
Exact Distributions / 3.1.0.: |
Return Periods of Largest and Large Values / 3.1.2.: |
Quantiles of Extremes / 3.1.3.: |
Characteristic Extremes / 3.1.4.: |
The Extremal Intensity Function / 3.1.5.: |
The Mode / 3.1.6.: |
The Maximum of the Mean Largest Value / 3.1.7.: |
Extremal Statistics / 3.2.: |
Absolute Extreme Values / 3.2.0.: |
Exact Distribution of Range / 3.2.2.: |
The Mean Range / 3.2.3.: |
The Range as Tolerance Limit / 3.2.4.: |
The Maximum of the Mean Range / 3.2.5.: |
Exact Distribution of the Midrange / 3.2.6.: |
Asymptotic Independence of Extremes / 3.2.7.: |
The Extremal Quotient / 3.2.8.: |
Analytical Study of Extremes / Chapter 4: |
The Exponential Type / 4.1.: |
Largest Value for the Exponential Distribution / 4.1.0.: |
Order Statistics for the Exponential Distribution / 4.1.2.: |
L'Hopital's Rule / 4.1.3.: |
Definition of the Exponential Type / 4.1.4.: |
The Three Classes / 4.1.5.: |
The Logarithmic Trend / 4.1.6.: |
The Characteristic Product / 4.1.7.: |
Extremes of the Exponential Type / 4.2.: |
The Logistic Distribution / 4.2.0.: |
Normal Extremes, Numerical Values / 4.2.2.: |
Analysis of Normal Extremes / 4.2.3.: |
Normal Extreme Deviates / 4.2.4.: |
Gamma Distribution / 4.2.5.: |
Logarithmic Normal Distribution / 4.2.6.: |
The Normal Distribution as a Distribution of Extremes / 4.2.7.: |
The Cauchy Type / 4.3.: |
The Exponential Type and the Existence of Moments / 4.3.0.: |
Pareto's Distribution / 4.3.2.: |
Definition of the Pareto and the Cauchy Types / 4.3.3.: |
Extremal Properties / 4.3.4.: |
Other Distributions without Moments / 4.3.5.: |
The First Asymptotic Distribution / 4.3.6.: |
The Three Asymptotes / 5.1.: |
Preliminary Derivation / 5.1.0.: |
The Stability Postulate / 5.1.2.: |
Outline of Other Derivations / 5.1.3.: |
Interdependence / 5.1.4.: |
The Double Exponential Distribution / 5.2.: |
Derivations / 5.2.0.: |
The Methods of Cramer and Von Mises / 5.2.2.: |
Mode and Median / 5.2.3.: |
Generating Functions / 5.2.4.: |
Standard and Mean Deviations / 5.2.5.: |
Probability Paper and Return Period / 5.2.6.: |
Comparison with Other Distributions / 5.2.7.: |
Barricelli's Generalization / 5.2.8.: |
Extreme Order Statistics / 5.3.: |
Distribution of the MTH Extreme / 5.3.0.: |
Probabilities of the mth Extreme / 5.3.2.: |
Cramer's Distribution of MTH Extremes / 5.3.3.: |
Extreme Distances / 5.3.5.: |
The Largest Absolute Value and the Two Sample Problem / 5.3.6.: |
Uses of the First Asymptote / Chapter 6: |
Order Statistics from the Double Exponential Distribution / 6.1.: |
Maxima of Largest Values / 6.1.0.: |
Minima of Largest Values / 6.1.2.: |
Consecutive Modes / 6.1.3.: |
Consecutive Means and Variances / 6.1.4.: |
Standard Errors / 6.1.5.: |
Extension of the Control Band / 6.1.6.: |
The Control Curve of Dick and Darwin / 6.1.7.: |
Estimation of Parameters / 6.2.: |
Exponential and Normal Extremes / 6.2.0.: |
Use of Order Statistics / 6.2.2.: |
Estimates for Probability Paper / 6.2.3.: |
Sufficient Estimation Functions / B. F. Kimball6.2.4.: |
Maximum Likelihood Estimations / 6.2.5.: |
Approximate Solutions / 6.2.6.: |
Asymptotic Variance of a Forecast / 6.2.7.: |
Numerical Examples / 6.3.: |
Floods / 6.3.0.: |
The Design Flood / 6.3.2.: |
Meteorological Examples / 6.3.3.: |
Application to Aeronautics / 6.3.4.: |
Oldest Ages / 6.3.5.: |
Breaking Strength / 6.3.6.: |
Breakdown Voltage / 6.3.7.: |
Applications to Naval Engineering / 6.3.8.: |
An Application to Geology / 6.3.9.: |
The Second and Third Asymptotes / Chapter 7: |
The Second Asymptote / 7.1.: |
Frechet's Derivation / 7.1.0.: |
Averages and Moments / 7.1.2.: |
Estimation of the Parameters / 7.1.4.: |
The Increase of the Extremes / 7.1.5.: |
Generalization / 7.1.6.: |
Applications / 7.1.7.: |
The Third Asymptote / 7.1.8.: |
The Von Mises Derivation / 7.2.0.: |
Other Derivations / 7.2.2.: |
Averages and Moments of Smallest Values / 7.2.3.: |
Special Cases / 7.2.4.: |
The 15 Relations Among the 3 Asymptotes / 7.2.5.: |
Applications of the Third Asymptote / 7.3.: |
Estimation of the Three Parameters / 7.3.0.: |
Estimation of Two Parameters / 7.3.2.: |
Analytical Examples / 7.3.3.: |
Droughts / 7.3.4.: |
Fatigue Failures / 7.3.5.: |
The Range / Chapter 8: |
Asymptotic Distributions of Range and Midrange / 8.1.: |
The Range of Minima / 8.1.0.: |
Generating Function of the Range / 8.1.2.: |
The Reduced Range / 8.1.3.: |
Asymptotic Distribution of the Midrange / 8.1.4.: |
A Bivariate Transformation / 8.1.5.: |
Asymptotic Distribution of the Range / 8.1.6.: |
Boundary Conditions / 8.1.7.: |
Extreme Ranges / 8.1.8.: |
Extremal Quotient and Geometric Range / 8.1.9.: |
Definitions / 8.2.0.: |
The Geometric Range / 8.2.2.: |
The Midrange / 8.3.: |
The Parameters in the Distribution of Range / 8.3.2.: |
Normal Ranges / 8.3.3.: |
Estimation of Initial Standard Deviation / 8.3.4.: |
Climatological Examples / 8.3.5.: |
Bibliography |
Index |
Aims and Tools / Chapter 1: |
Aims / 1.0.: |
Conditions / 1.0.1.: |