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| Chapter One: AIMS AND TOOLS 1.0. Aims 1.0.1. Conditions 1.0.2. History 1.0.3. The Flood Problem 1.0.4. Methodology 1.0.5. Arrangement of Contents 1.1. General Tools 1.1.1. Linear Transformations 1.1.2. Other Transformations 1.1.3. Symmetry 1.1.4. Measures of Dispersion 1.1.5. Moments 1.1.6. Generating Function 1.1.7. Convolution 1.1.8. The Gamma Function 1.1.9. The Logarithmic Normal Distribution 1.2. Specific Tools 1.2.0. Problems 1.2.1. The Intensity Function 1.2.2. The Distribution of Repeated Occurrences 1.2.3. Analysis of Return Periods 1.2.4. "Observed" Distributions 1.2.5. Construction of Probability Papers 1.2.6. The Plotting Problem 1.2.7. Conditions for Plotting Positions 1.2.8. Fitting Straight Lines on Probability Papers 1.2.9. Application to the Normal Distribution Chapter Two: ORDER STATISTICS AND THEIR EXCEEDANCES 2.1. Order Statistics 2.1.0. Problems 2.1.1. Distributions 2.1.2. Averages 2.1.3. Distribution of Frequencies 2.1.4. Asymptotic Distribution of ruth Central Values 2.1.5. The Order Statistic with Minimum Variance 2.1.6. Control Band 2.1.7. Joint Distribution of Order Statistics 2.1.8. Distribution of Distances 2.2. The Distribution of Exceedances 2.2.0. Introduction 2.2.1. Distribution of the Number of Exceedances 2.2.2. Moments 2.2.3. The Median 2.2.4. The Probability of Exceedances as Tolerance Limit 2.2.5. Extrapolation from Small Samples 2.2.6. Normal and Rare Exceedances 2.2.7. Frequent Exceedances 2.2.8. Summary Chapter Three: EXACT DISTRIBUTION OF EXTREMES 3.1. Averages of Extremes 3.1.0. Problems 3.1.1. Exact Distributions 3.1.2. Return Periods of Largest and Large Values 3.1.3. Quantiles of Extremes 3.1.4. Characteristic Extremes 3.1.5. The Extremal Intensity Function 3.1.6. The Mode 3.1.7. Moments 3.1.8. The Maximum of the Mean Largest Value 3.2. Extremal Statistics 3.2.0. Problems 3.2.1. Absolute Extreme Values 3.2.2. Exact Distribution of Range 3.2.3. The Mean Range 3.2.4. The Range as Tolerance Limit 3.2.5. The Maximum of the Mean Range 3.2.6. Exact Distribution of the Midrange 3.2.7. Asymptotic Independence of Extremes 3.2.8. The Extremal Quotient Chapter Four :ANALYTICAL STUDY OF EXTREMES Chapter Six : USES OF THE FIRST ASYMPTOTE Chapter Seven:THE SECOND AND THIRD ASYMPTOTES Chapter Eight:THE RANGE Summary Bibliography Index |
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