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| Aims and Tools | |
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| Aims | |
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| Conditions | |
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| History | |
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| The Flood Problem | |
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| Methodology | |
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| Arrangement of Contents | |
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| General Tools | |
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| Linear Transformations | |
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| Other Transformations | |
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| Symmetry | |
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| Measures of Dispersion | |
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| Moments | |
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| Generating Function | |
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| Convolution | |
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| The Gamma Function | |
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| The Logarithmic Normal Distribution | |
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| Specific Tools | |
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| Problems | |
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| The Intensity Function | |
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| The Distribution of Repeated Occurrences | |
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| Analysis of Return Periods | |
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| "Observed" Distributions | |
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| Construction of Probability Papers | |
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| The Plotting Problem | |
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| Conditions for Plotting Positions | |
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| Fitting Straight Lines on Probability Papers | |
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| Application to the Normal Distribution | |
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| Order Statistics and Their Exceedances | |
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| Order Statistics | |
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| Problems | |
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| Distributions | |
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| Averages | |
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| Distribution of Frequencies | |
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| Asymptotic Distribution of mth Central Values | |
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| The Order Statistic with Minimum Variance | |
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| Control Band | |
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| Joint Distribution of Order Statistics | |
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| Distribution of Distances | |
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| The Distribution of Exceedances | |
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| Introduction | |
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| Distribution of the Number of Exceedances | |
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| Moments | |
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| The Median | |
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| The Probability of Exceedances as Tolerance Limit | |
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| Extrapolation from Small Samples | |
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| Normal and Rare Exceedances | |
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| Frequent Exceedances | |
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| Summary | |
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| Exact Distribution of Extremes | |
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| Averages of Extremes | |
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| Problems | |
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| Exact Distributions | |
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| Return Periods of Largest and Large Values | |
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| Quantiles of Extremes | |
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| Characteristic Extremes | |
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| The Extremal Intensity Function | |
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| The Mode | |
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| Moments | |
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| The Maximum of the Mean Largest Value | |
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| Extremal Statistics | |
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| Problems | |
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| Absolute Extreme Values | |
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| Exact Distribution of Range | |
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| The Mean Range | |
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| The Range as Tolerance Limit | |
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| The Maximum of the Mean Range | |
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| Exact Distribution of the Midrange | |
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| Asymptotic Independence of Extremes | |
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| The Extremal Quotient | |
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| Analytical Study of Extremes | |
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| The Exponential Type | |
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| Problems | |
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| Largest Value for the Exponential Distribution | |
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| Order Statistics for the Exponential Distribution | |
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| L'Hopital's Rule | |
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| Definition of the Exponential Type | |
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| The Three Classes | |
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| The Logarithmic Trend | |
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| The Characteristic Product | |
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| Extremes of the Exponential Type | |
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| Problems | |
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| The Logistic Distribution | |
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| Normal Extremes, Numerical Values | |
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| Analysis of Normal Extremes | |
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| Normal Extreme Deviates | |
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| Gamma Distribution | |
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| Logarithmic Normal Distribution | |
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| The Normal Distribution as a Distribution of Extremes | |
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| The Cauchy Type | |
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| Problems | |
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| The Exponential Type and the Existence of Moments | |
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| Pareto's Distribution | |
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| Definition of the Pareto and the Cauchy Types | |
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| Extremal Properties | |
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| Other Distributions without Moments | |
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| Summary | |
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| The First Asymptotic Distribution | |
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| The Three Asymptotes | |
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| Introduction | |
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| Preliminary Derivation | |
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| The Stability Postulate | |
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| Outline of Other Derivations | |
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| Interdependence | |
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| The Double Exponential Distribution | |
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| Introduction | |
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| Derivations | |
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| The Methods of Cramer and Von Mises | |
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| Mode and Median | |
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| Generating Functions | |
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| Standard and Mean Deviations | |
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| Probability Paper and Return Period | |
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| Comparison with Other Distributions | |
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| Barricelli's Generalization | |
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| Extreme Order Statistics | |
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| Problems | |
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| Distribution of the MTH Extreme | |
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| Probabilities of the mth Extreme | |
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| Generating Functions | |
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| Cramer's Distribution of MTH Extremes | |
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| Extreme Distances | |
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| The Largest Absolute Value and the Two Sample Problem | |
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| Uses of the First Asymptote | |
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| Order Statistics from the Double Exponential Distribution | |
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| Problems | |
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| Maxima of Largest Values | |
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| Minima of Largest Values | |
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| Consecutive Modes | |
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| Consecutive Means and Variances | |
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| Standard Errors | |
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| Extension of the Control Band | |
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| The Control Curve of Dick and Darwin | |
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| Estimation of Parameters | |
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| Problems | |
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| Exponential and Normal Extremes | |
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| Use of Order Statistics | |
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| Estimates for Probability Paper | |
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| Sufficient Estimation Functions | |
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| Maximum Likelihood Estimations | |
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| Approximate Solutions | |
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| Asymptotic Variance of a Forecast | |
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| Numerical Examples | |
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| Problems | |
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| Floods | |
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| The Design Flood | |
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| Meteorological Examples | |
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| Application to Aeronautics | |
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| Oldest Ages | |
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| Breaking Strength | |
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| Breakdown Voltage | |
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| Applications to Naval Engineering | |
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| An Application to Geology | |
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| The Second and Third Asymptotes | |
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| The Second Asymptote | |
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| Problems | |
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| Frechet's Derivation | |
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| The Cauchy Type | |
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| Averages and Moments | |
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| Estimation of the Parameters | |
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| The Increase of the Extremes | |
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| Generalization | |
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| Applications | |
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| Summary | |
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| The Third Asymptote | |
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| Introduction | |
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| The Von Mises Derivation | |
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| Other Derivations | |
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| Averages and Moments of Smallest Values | |
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| Special Cases | |
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| The Increase of the Extremes | |
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| The 15 Relations Among the 3 Asymptotes | |
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| Applications of the Third Asymptote | |
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| Problems | |
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| Estimation of the Three Parameters | |
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| Estimation of Two Parameters | |
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| Analytical Examples | |
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| Droughts | |
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| Fatigue Failures | |
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| The Range | |
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| Asymptotic Distributions of Range and Midrange | |
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| Problems | |
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| The Range of Minima | |
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| Generating Function of the Range | |
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| The Reduced Range | |
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| Asymptotic Distribution of the Midrange | |
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| A Bivariate Transformation | |
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| Asymptotic Distribution of the Range | |
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| Boundary Conditions | |
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| Extreme Ranges | |
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| Summary | |
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| Extremal Quotient and Geometric Range | |
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| Problems | |
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| Definitions | |
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| The Extremal Quotient | |
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| The Geometric Range | |
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| Applications | |
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| Problems | |
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| The Midrange | |
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| The Parameters in the Distribution of Range | |
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| Normal Ranges | |
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| Estimation of Initial Standard Deviation | |
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| Climatological Examples | |
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| Summary | |
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| Bibliography | |
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| Index | |