Statistics of extremes

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Statistics of extremes / by E.J. Gumbel

資料種別:: 図書
出版情報:: New York : Columbia University Press, 1958
形態:: xx, 375 p. ; 24 cm
著者名:: Gumbel, Emil Julius, 1891- <DA01014000>
ISBN:: 9780231021906 [0231021909]
書誌ID:: BA0454473X

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注記:

Bibliography: p. [349]-371
Includes index

主題:

Mathematical statistics; Maxima and minima

言語:

英語

目次情報:

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.：

History / 1.0.2.：

The Flood Problem / 1.0.3.：

Methodology / 1.0.4.：

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