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1.

図書
図書
1. Statistics of extremes
by E.J. Gumbel
出版情報: New York : Columbia University Press, 1958  xx, 375 p. ; 24 cm
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目次情報: 続きを見る
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.：
2.

図書
図書
2. Trigonometric series. 2nd ed (v. 1 ; v. 2)
A. Zygmund
出版情報: Cambridge : Cambridge University Press, 1959  2 v. (ix, 383, 354 p) ; 27 cm
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3.

図書
図書
3. Topologie. 3e éd., corr. (t. 1 ; t. 2)
Casimir Kuratowski
出版情報: Warszawa : Nakładem Polskiego Towarzystwa Matematycznego , New York : Hafner Publishing, c1952  2 v. ; 25 cm
シリーズ名: Monografie matematyczne ; t. 20, 21
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4.

図書
図書
4. Asymptotic expansions
A. Erdélyi
出版情報: New York : Dover Publications, 1956  vi, 108 p. ; 21 cm
シリーズ名: Dover books on advanced mathematics
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目次情報: 続きを見る
Introduction
References
Asymptotic Series / Chapter I：
O-symbols / 1.1：
Asymptotic sequences / 1.2：
Asymptotic expansions / 1.3：
Linear operations with asymptotic expansions / 1.4：
Other operations with asymptotic expansions / 1.5：
Asymptotic power series / 1.6：
Summation of asymptotic series / 1.7：
Integrals / Chapter II：
Integration by parts / 2.1：
Laplace integrals / 2.2：
Critical points / 2.3：
Laplace's method / 2.4：
The method of steepest descents / 2.5：
Airy's integral / 2.6：
Further examples / 2.7：
Fourier integrals / 2.8：
The method of stationary phase / 2.9：
Singularities of Differential Equations / Chapter III：
Classification of singularities / 3.1：
Normal solutions / 3.2：
The integral equation and its solution / 3.3：
Asymptotic expansions of the solutions / 3.4：
Complex variable / 3.5：
Stokes' phenomenon
Bessel functions of order zero / 3.6：
Differential Equations with a Large Parameter / Chapter IV：
Liouville's problem / 4.1：
Formal solutions / 4.2：
Asymptotic solutions / 4.3：
Application to Bessel functions / 4.4：
Transition points / 4.5：
Airy functions / 4.6：
Asymptotic solutions valid in the transition region / 4.7：
Uniform asymptotic representations of Bessel functions / 4.8：
Introduction
References
Asymptotic Series / Chapter I：
5.

図書
図書
5. Topics in number theory (v. 1 ; v. 2)
by William Judson LeVeque
出版情報: Reading, Mass. : Addison-Wesley, c1956  2 v. ; 24 cm
シリーズ名: Addison-Wesley mathematics series
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6.

図書
図書
6. Sample survey methods and theory (v. 1 ; v. 2)
by Morris H. Hansen, William N. Hurwitz and William G. Madow
出版情報: New York : Wiley, c1953  v. ; 23 cm
シリーズ名: Wiley publications in statistics
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目次情報:
Vol. 1. Methods and applications
Vol. 2. Theory
Vol. 1. Methods and applications
Vol. 2. Theory
7.

図書
図書
7. The theory of functions of a real variable and the theory of Fourier's series (v. 1 ; v. 2)
by E.W. Hobson
出版情報: New York : Dover Publications, 1957  2 v. ; 22 cm
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8.

図書
図書
8. Infinite sequences and series
by Konrad Knopp ; translated by Frederick Bagemihl
出版情報: New York : Dover Publications, c1956  v, 186 p. ; 21 cm
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目次情報: 続きを見る
Foreword
Introduction and Prerequisites / Chapter 1：
Preliminary remarks concerning sequences and series / 1.1：
Real and complex numbers / 1.2：
Sets of numbers / 1.3：
Functions of a real and of a complex variable / 1.4：
Sequences and Series / Chapter 2：
Arbitrary sequences / 2.1：
Null sequences
Sequences and sets of numbers / 2.2：
Convergence and divergence / 2.3：
Cauchy's limit theorem and its generalizations / 2.4：
The main tests for sequences / 2.5：
Infinite series / 2.6：
The Main Tests for Infinite Series / Chapter 3：
Operating with Convergent Series
Series of positive terms: The first main test and the comparison tests of the first and second kind / 3.1：
The radical test and the ratio test / 3.2：
Series of positive, monotonically decreasing terms / 3.3：
The second main test / 3.4：
Absolute convergence / 3.5：
Operating with convergent series / 3.6：
Infinite products / 3.7：
Power Series / Chapter 4：
The circle of convergence / 4.1：
The functions represented by power series / 4.2：
Operating with power series / 4.3：
Expansion of composite functions
The inversion of a power series / 4.4：
Development of the Theory of Convergence / Chapter 5：
The theorems of Abel, Dini, and Pringsheim / 5.1：
Scales of convergence tests / 5.2：
Abel's partial summation / 5.3：
Lemmas
Special comparison tests of the second kind / 5.4：
Abel's and Dirichlet's tests and their generalizations / 5.5：
Series transformations / 5.6：
Multiplication of series / 5.7：
Expansion of the Elementary Functions / Chapter 6：
List of the elementary functions / 6.1：
The rational functions / 6.2：
The exponential function and the circular functions / 6.3：
The logarithmic function / 6.4：
The general power and the binomial series / 6.5：
The cyclometric functions / 6.6：
Numerical and Closed Evaluation of Series / Chapter 7：
Statement of the problem / 7.1：
Numerical evaluations and estimations of remainders / 7.2：
Closed evaluations Bibliography / 7.3：
Index
Foreword
Introduction and Prerequisites / Chapter 1：
Preliminary remarks concerning sequences and series / 1.1：
9.

図書
図書
9. An introduction to probability theory and its applications. 2nd ed (v. 1 ; v. 2)
William Feller
出版情報: New York : Wiley, c1957-c1971  2 v. ; 24 cm
シリーズ名: Wiley series in probability and mathematical statistics ; . Probability and mathematical statistics
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10.

図書
図書
10. Proceedings of the International Congress of Mathematicians, 1954 : Amsterdam, September 2-September 9 (v. 1 ; v. 2 ; v. 3)
[editorial committee, Johan C.H. Gerretsen, Johannes de Groot]
出版情報: Groningen : Noordhoff , Amsterdam : North-Holland Pub., 1954-1957  3 v. ; 25 cm
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