Roger B. Nelsen
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Mathematics
Roger B. Nelsen's Degrees
- PhD Mathematics Stanford University
- Masters Mathematics Stanford University
- Bachelors Mathematics University of California, Davis
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(Suggest an Edit or Addition)Roger B. Nelsen's Published Works
Number of citations in a given year to any of this author's works
Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author
Published Works
- An Introduction to Copulas (1998) (5621)
- An Introduction to Copulas (Springer Series in Statistics) (2006) (1013)
- On the relationship between Spearman's rho and Kendall's tau for pairs of continuous random variables (2007) (203)
- Best-possible bounds for the distribution of a sum — a problem of Kolmogorov (1987) (191)
- Dependence in probabilistic modeling, Dempster-Shafer theory, and probability bounds analysis. (2004) (153)
- On the characterization of a class of binary operations on distribution functions (1993) (152)
- Properties of a one-parameter family of bivariate distributions with specified marginals (1986) (103)
- On the construction of copulas and quasi-copulas with given diagonal sections (2008) (102)
- Kendall distribution functions (2003) (95)
- Copulas and Association (1991) (93)
- Best-possible bounds on sets of bivariate distribution functions (2004) (91)
- Nonparametric measures of multivariate association (1996) (82)
- Proofs Without Words: Exercises in Visual Thinking (2020) (78)
- Proofs Without Words (1993) (75)
- Concordance and Copulas: A Survey (2002) (74)
- Extremes of nonexchangeability (2007) (71)
- Copulas Constructed from Diagonal Sections (1997) (71)
- BOUNDS ON BIVARIATE DISTRIBUTION FUNCTIONS WITH GIVEN MARGINS AND MEASURES OF ASSOCIATION (2001) (68)
- Bivariate copulas with cubic sections (1997) (64)
- Dependence and Order in Families of Archimedean Copulas (1997) (63)
- The lattice-theoretic structure of sets of bivariate copulas and quasi-copulas (2005) (61)
- Encyclopaedia of Mathematics, Supplement III (2002) (59)
- The Bertino Family of Copulas (2002) (57)
- Some concepts of bivariate symmetry (1993) (56)
- Properties and applications of copulas : A brief survey (2004) (49)
- Concordance and Gini's measure of association (1998) (49)
- Worst VaR scenarios with given marginals and measures of association (2009) (48)
- Discrete bivariate distributions with given marginals and correlation (1987) (47)
- Copulas, Characterization, Correlation, and Counterexamples (1995) (45)
- Math Made Visual: Creating Images for Understanding Mathematics (2006) (44)
- Copulas with fractal supports (2005) (43)
- On measures of association as measures of positive dependence (1992) (42)
- Robust Fits for Copula Models (2007) (41)
- Derivability of some operations on distribution functions (1996) (40)
- Distribution functions of copulas: a class of bivariate probability integral transforms (2001) (39)
- Summation by Parts (1992) (37)
- Some properties of Schur-constant survival models and their copulas (2005) (34)
- Charming Proofs: A Journey into Elegant Mathematics (2010) (34)
- Some New Properties of Quasi-Copulas (2002) (34)
- Copulas and quasi-copulas: An introduction to their properties and applications (2005) (32)
- A Comparison of Bounds on Sets of Joint Distribution Functions Derived from Various Measures of Association (2005) (30)
- Correlation, Regression Lines, and Moments of Inertia (1998) (26)
- Directional dependence in multivariate distributions (2012) (25)
- An Invitation to Proofs Without Words (2009) (25)
- Quasi-copulas and signed measures (2010) (23)
- Heron's Formula via Proofs without Words (2001) (23)
- Multivariate copulas, quasi-copulas and lattices (2011) (22)
- Proofs Without Words III: Further Exercises in Visual Thinking (2015) (18)
- A Visual Proof of the Erdős-Mordell Inequality (2007) (18)
- When Less is More: Visualizing Basic Inequalities (2009) (17)
- Multivariate Archimedean Quasi-Copulas (2002) (16)
- A new index to measure positive dependence in trivariate distributions (2013) (15)
- Best-possible bounds on the set of copulas with given degree of non-exchangeability (2014) (15)
- Probability and Random Variables: A Beginner's Guide (2001) (14)
- Dependence Modeling with Archimedean Copulas (2005) (14)
- Chains in Power Sets (1991) (14)
- Kendall distribution functions and associative copulas (2009) (14)
- Icons of Mathematics: An Exploration of Twenty Key Images (2020) (12)
- Isaac Newton: Credit Where Credit Won't Do (1994) (12)
- On the Diagonals of a Cyclic Quadrilateral (2007) (11)
- A Visual Proof of the Erd˝ os-Mordell Inequality (2007) (11)
- Random displacements of regularly spaced events (1970) (10)
- A Mathematical Space Odyssey: Solid Geometry in the 21st Century (2015) (9)
- More exercises in visual thinking (2000) (8)
- Independence results for multivariate tail dependence coefficients (2016) (8)
- Icons of Mathematics (2011) (7)
- Proofs Without Words II (2018) (7)
- Consequences of the memoryless property for random variables (1987) (7)
- Proof Without Words: The Area of an Arbelos (2002) (6)
- Proof Without Words: Four Squares with Constant Area (2004) (6)
- Geometric Proofs of the Weitzenböck and Hadwiger-Finsler Inequalities (2008) (6)
- How close are pairwise and mutual independence (2012) (6)
- The Structure of the Class of Maximum Tsallis-Havrda-Chavát Entropy Copulas (2016) (5)
- On the relationship between Spearman’s rho and Kendall’s tau for continuous random variables (2006) (5)
- Proof without Words: The Arithmetic-Logarithmic-Geometric Mean Inequality (1995) (5)
- The Double-Angle Formulas (1989) (5)
- Symmetries of random discrete copulas (2008) (5)
- A Mathematical Space Odyssey (2015) (5)
- Proof without Words: The Harmonic Mean-Geometric Mean-Arithmetic Mean-Root Mean Square Inequality. (1987) (5)
- Euler's Triangle Inequality via Proofs Without Words (2008) (5)
- Randomly Delayed Appointment Streams (1968) (4)
- An Improved Remainder Estimate for Use with the Integral Test (2003) (4)
- Cameos for Calculus: Visualization in the First-Year Course (2015) (4)
- Proof Without Words: Steiner's Problem on the Number e (2009) (4)
- Computing an expected hitting time for the 3-urn Ehrenfest model via electric networks (2017) (4)
- Proof Without Words: Sums of Triangular Numbers (2005) (4)
- A CHARACTERIZATION OF FARLIE-GUMBEL-MORGENSTERN DISTRIBUTIONS VIA SPEARMAN'S RHO AND CHI-SQUARE DIVERGENCE (2016) (4)
- Proof without Words: Geometric Series (1994) (4)
- Proof without Words: Aristarchus' Inequalities (1993) (4)
- Proof Without Words: Every Octagonal Number Is the Difference of Two Squares (2004) (4)
- A Cornucopia of Quadrilaterals (2020) (4)
- Pairwise and Global Dependence in Trivariate Copula Models (2014) (4)
- Visual Gems of Number Theory (2008) (4)
- Proof Without Words: A Reciprocal Pythagorean Theorem (2009) (3)
- Proof without Words: The Sum of a Positive Number and Its Reciprocal Is at Least Two (four proofs) (1994) (3)
- Elementary Problems: E3059-E3063 (1984) (3)
- Further Integral Skinning with Applications (2018) (3)
- Proof without Words: Sum of Reciprocals of triangular numbers (1991) (3)
- Proof Without Words: Candido's Identity (2005) (3)
- Completing the square (2015) (3)
- Proof without Words: The Cauchy-Schwarz Inequality (1994) (3)
- Proof without Words: Integration by Parts (1991) (2)
- Icons of Mathematics: The Bride's Chair (2011) (2)
- Proof Without Words: A Triangular Identity (1994) (2)
- Nuggets of Number Theory (2018) (2)
- Proof Without Words: A Trigonometric Identity for sec x + tan x (2015) (2)
- Proof Without Words: The Area of a Salinon (2002) (2)
- Paintings, Plane Tilings, & Proofs (2003) (2)
- Proof Without Words: Square Triangular Numbers and Almost Isosceles Pythagorean Triples (2016) (2)
- Proof Without Words: Infinitely Many Almost-Isosceles Pythagorean Triples Exist (2016) (2)
- Proof without Words: An Arctangent Identity and Series (1991) (2)
- On Candido's Identity (2007) (2)
- Proof Without Words: Padoa's Inequality (Alessandro Padoa, 1868–1937) (2006) (2)
- Proof Without Words: The Formulas of Hutton and Strassnitzky (2013) (2)
- Methods of Constructing Copulas (1999) (2)
- Proof Without Words: The Golden Ratio (2016) (2)
- Icons of Mathematics: Zhou Bi Suan Jing (2011) (2)
- Math Made Visual: References (2006) (2)
- Bounds for distribution functions of sums of squares and radial errors. (1991) (2)
- Paintings, Plane Tilings and Proofs (2006) (1)
- Proof Without Words: Diophantus of Alexandria's Sum of Squares Identity (1993) (1)
- The Calculus Collection: A Resource for AP and Beyond (2010) (1)
- The Probability that the “Sum of the Rounds” Equals the “Round of the Sum” (1987) (1)
- Even Perfect Numbers End in 6 or 28 (2018) (1)
- Proof Without Words: Another Pythagorean Theorem (2021) (1)
- The Relationship Between Hyperbolic and Exponential Functions (1988) (1)
- Proof Without Words: Perfect Numbers and Triangular Numbers (2016) (1)
- Elementary Proofs of the Trigonometric Inequalities of Huygens, Cusa, and Wilker (2020) (1)
- Proof Without Words: An Alternating Series (2012) (1)
- Proof without Words Corollary: Sums of Squares (1990) (1)
- The Root Mean Square-Arithmetic Mean-Geometric Mean-Harmonic Mean Inequality (1989) (1)
- Periodic Continued Fractions Via a Proof Without Words (2018) (1)
- Proof without Words: Squares of Triangular Numbers (1990) (1)
- Proof without words: Regle des Nombres Moyens (1994) (1)
- Proof Without Words: The Difference of Consecutive Integer Cubes Is Congruent to 1 Modulo 6 (2014) (1)
- Proof Without Words: Bernoulli's Inequality (two proofs) (1996) (1)
- Proof Without Words: A Trigonometric Proof of the Arithmetic Mean–Geometric Mean Inequality (2015) (1)
- Proof Without Words: Inequalities for Two Numbers Whose Sum Is One (2011) (1)
- Almost Equilateral Heronian Triangles (2020) (1)
- Proof without Words: Alternating Sums of Triangular Numbers (1995) (1)
- Symmetry and Integration (1995) (1)
- Proof Without Words: The Cube as an Arithmetic Sum (2003) (1)
- Proof without Words: Consecutive sums of consecutive integers (1990) (1)
- Mathematical ENQUIRER (2007) (1)
- Proof without words: On a property of the sequence of odd integers (Galileo, 1615) (1995) (1)
- Proof Without Words: Inclusion-Exclusion for Triangular Numbers (2006) (1)
- A Geometric Proof of Machin's Formula (1990) (1)
- MYTHS ABOUT CORRELATIONS AND DEPENDENCIES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 AND THEIR IMPLICATIONS FOR RISK ANALYSIS (2005) (1)
- The harmonic series and the Euler-Mascheroni constant (2015) (0)
- Derivatives of area and volume (2015) (0)
- Proof Without Words: A Right Triangle Identity (2016) (0)
- Solutions to the Pell Equation x 2 − Ny 2 = 1 (2022) (0)
- Proof Without Words: Centered Triangular Numbers (2015) (0)
- Illustrating a telescoping series (2015) (0)
- The hyperbolic functions I: Definitions (2015) (0)
- Charming Proofs: Points in the Plane (2010) (0)
- The AM-GM inequality for n positive numbers (2015) (0)
- Geometric Series V (2015) (0)
- Proof Without Words: Ptolemy's Inequality (2014) (0)
- Approximating π with Maclaurin series (2015) (0)
- Definitions and Basic Properties (1999) (0)
- Icons of Mathematics: Napoleon's Triangles (2011) (0)
- Proof Without Words: A Triangular Sum (2005) (0)
- Representing Numbers by Lengths of Segments (2006) (0)
- Icons of Mathematics: Venn Diagrams (2011) (0)
- Machin’s Formula Via a Proof Without Words (2021) (0)
- Proof Without Words: The Pentagon-Hexagon-Decagon Identity (2016) (0)
- Hints and Solutions to the Challenges (2006) (0)
- Icons of Mathematics: Arcs and Angles (2011) (0)
- Icons of Mathematics: References (2011) (0)
- Proof Without Words: A Sine Identity for Triangles (2014) (0)
- Napier's inequality and the limit for e (2015) (0)
- Charming Proofs: Geometry in Three Dimensions (2010) (0)
- Basic trigonometric identities (2015) (0)
- Representing positive numbers as areas or volumes (2011) (0)
- Does shell volume equal disk volume (2015) (0)
- The nth root of n! and another limit for e (2015) (0)
- Math Made Visual: Geometric Dissections (2006) (0)
- Proof Without Words: Sums of Every Third Triangular Number (2015) (0)
- A geometric illustration of the limit for e (2015) (0)
- Proof Without Words: Consecutive Powerful Numbers (2022) (0)
- Visualization by Inclusion (2006) (0)
- Proof Without Words: New Pythagorean-like Theorems (2010) (0)
- Proof without Words: Volume of a Frustum of a Square Pyramid (1995) (0)
- Approximating π with the limit of (sin t)/t (2015) (0)
- Proof Without Words: Tangents of Multiples of π/24 (2022) (0)
- Integration by parts (2015) (0)
- Means and the mean value theorem (2015) (0)
- Math Made Visual: Visualization in the Classroom (2006) (0)
- Icons of Mathematics: Preface (2011) (0)
- Representing positive numbers as lengths of segments (2011) (0)
- Proof Without Words: The Area of a Regular Dodecagon (2015) (0)
- The Maclaurin Inequality and Rectangular Boxes (2017) (0)
- Pythagorean Triples and (2021) (0)
- Proof Without Words: Runs of Triangular Numbers (2012) (0)
- Icons of Mathematics: Similar Figures (2011) (0)
- Escaping from the Plane (2006) (0)
- Geometric differentiation of geometric series (2015) (0)
- Letter to the Editor: Isosceles Dissections (2009) (0)
- Identifying Key Elements (2006) (0)
- Means, Milne’s inequality, and quadrilateral area (2021) (0)
- Sums ofOdd Integers IV (2015) (0)
- Using incircles and circumcircles (2011) (0)
- Proof Without Words: Nested Square Roots (2017) (0)
- Visualizing the derivative (2015) (0)
- Are all parabolas similar (2015) (0)
- Proof Without Words: Nearly Cubic Pythagorean Boxes (2016) (0)
- Charming Proofs: Distinguished Numbers (2010) (0)
- Multi-Polygonal Numbers (2016) (0)
- A Panoply of Polygons (2023) (0)
- Icons of Mathematics: The Right Triangle (2011) (0)
- Which is larger, eπ or πe? ab or ba? (2015) (0)
- Proof Without Words: Sums of Odd and Even Squares (2015) (0)
- Illustrating applications of the monotone sequence theorem (2015) (0)
- The product rule (2015) (0)
- Proof Without Words: A Sum and Product of Three Tangents (2002) (0)
- Proof without Words: Differentiated geometric series (1989) (0)
- The hyperbolic functions II: Are they circular? (2015) (0)
- Proof Without Words: The Sum of the Squares of Consecutive Triangular Numbers Is Triangular (1997) (0)
- Polar area and Cartesian area (2015) (0)
- ASSISTANT EDITORS ^^ZJLJ^~A)<& (2016) (0)
- Padovan and Perrin Identities by Rectangular Tilings (2023) (0)
- Proof Without Words: Lunes and the Regular Hexagon (2002) (0)
- Charming Proofs: The Quadrilaterals' Corner (2010) (0)
- Sine of a Sum or Difference (via the Law of Sines) (2015) (0)
- Using 3D Models (2006) (0)
- The conic sections (2015) (0)
- Icons of Mathematics: Polygonal Lines (2011) (0)
- Icons of Mathematics: Tiling (2011) (0)
- Icons of Mathematics: Polygons with Circles (2011) (0)
- The addition formulas for the sine and cosine (2015) (0)
- Proof without Words: A Monotone Sequence Bounded by e (1994) (0)
- Proof Without Words: President Garfield and the Cauchy–Schwarz Inequality (2015) (0)
- Ingenuity in 3D (2006) (0)
- Proof Without Words: Summing Squares by Counting Triangles (2014) (0)
- Proof Without Words: Perfect Numbers and Sums of Odd Cubes (2016) (0)
- Icons of Mathematics: Self-similar Figures (2011) (0)
- Charming Proofs: Curves Ahead (2010) (0)
- Charming Proofs: Solutions to the Challenges (2010) (0)
- Proof Without Words: Every Fourth Power Greater than One Is the Sum of Two Nonconsecutive Triangular Numbers (2006) (0)
- Charming Proofs: A Treasury of Triangle Theorems (2010) (0)
- Plato’s Approximation of Pi (2021) (0)
- Proof without Words: Sums of Consecutive Powers of Nine Are Sums of Consecutive Integers (1990) (0)
- Why is Simpson's rule exact for cubics? (2015) (0)
- Pi is Less Than Twice Phi (2021) (0)
- Sums of Consecutive Odd Numbers (2023) (0)
- The alternating series test (2015) (0)
- The conic sections revisited (2015) (0)
- Icons of Mathematics: Garfield's Trapezoid (2011) (0)
- Charming Proofs: The Enchantment of the Equilateral Triangle (2010) (0)
- Icons of Mathematics: Yin and Yang (2011) (0)
- Proof without Words: Five Means—and Their Means (1996) (0)
- Icons of Mathematics: Overlapping Figures (2011) (0)
- Math Made Visual: Representing Numbers by Volumes of Objects (2006) (0)
- Proof Without Words: The Triple Angle Sine and Cosine Formulas (2012) (0)
- Charming Proofs: Introduction (2010) (0)
- Charming Proofs: Additional Theorems, Problems, and Proofs (2010) (0)
- Proof Without Words: A Surprising Integer Result (2016) (0)
- Proof Without Words: Perfect Numbers Modulo 7 (2017) (0)
- Playing with Several Copies (2006) (0)
- Can the midpoint rule be improved (2015) (0)
- Charming Proofs: The Polygonal Playground (2010) (0)
- Icons of Mathematics: Solutions to the Challenges (2011) (0)
- Charming Proofs: Adventures in Tiling and Coloring (2010) (0)
- Proof Without Words: Each But Two Triangular Numbers Is a Sum of Three Triangular Numbers (2015) (0)
- The Hermite-Hadamard inequality (2015) (0)
- The limit of (sin t)/t (2015) (0)
- Golden Tiles and Arctangent Identities (2022) (0)
- The alternating harmonic series (2015) (0)
- The derivative of the arctangent (2015) (0)
- Approximating π with integration (2015) (0)
- Proof Without Words: Squares Modulo 3 (2013) (0)
- Squared Primes Modulo 24 (2020) (0)
- Icons of Mathematics: The Rectangular Hyperbola (2011) (0)
- Representing Numbers by Graphical Elements (2006) (0)
- The prismoidal formula (2015) (0)
- Combinatorial identities for Riemann sums (2015) (0)
- Employing graphs of functions (2011) (0)
- The chain rule (2015) (0)
- Charming Proofs: References (2010) (0)
- Means and optimization (2015) (0)
- Directional dependence in multivariate distributions (2011) (0)
- The quotient rule (2015) (0)
- Proof Without Words: Squares in Circles and Semicircles (2009) (0)
- Icons of Mathematics: Cevians (2011) (0)
- Proof without Words: The substitution to make a rational function of the sine and cosine (1989) (0)
- Arctangents of Fibonacci Ratios (2023) (0)
- Charming Proofs: A Garden of Integers (2010) (0)
- Math Made Visual: Representing Numbers by Areas of Plane Figures (2006) (0)
- Proof Without Words: Alternating Sums of Consecutive Squares (2014) (0)
- The derivative of the arcsine (2015) (0)
- The Pythagorean Theorem XIII (2015) (0)
- Polar area as a source of antiderivatives (2015) (0)
- Icons of Mathematics: Twenty Key Icons of Mathematics (2011) (0)
- The Arithmetic Mean–Geometric Mean Inequality VII (2015) (0)
- Identities for Pell Numbers: A Visual Sampler (2023) (0)
- When Less is More: Preface (2009) (0)
- Icons of Mathematics: Star Polygons (2011) (0)
- Proof Without Words: Pythagorean Quadruples (2014) (0)
- Icons of Mathematics: Tatami (2011) (0)
- is Composite for (2021) (0)
- Proof Without Words: Right Triangles and Geometric Series (2006) (0)
- Icons of Mathematics: The Semicircle (2011) (0)
- Employing non-isometric transformations (2011) (0)
- Charming Proofs: Preface (2010) (0)
- The geometry of geometric series (2015) (0)
- Icons of Mathematics: About the Authors (2011) (0)
- Icons of Mathematics: Two Circles (2011) (0)
- Inequalities and the existence of triangles (2011) (0)
- Proof Without Words: The Pythagorean Theorem with Equilateral Triangles (2012) (0)
- The midpoint rule is better than the trapezoidal rule (2015) (0)
- Math Made Visual: Area-preserving Transformations (2006) (0)
- Solids of revolution and the Cauchy-Schwarz inequality (2015) (0)
- PROOF WITHOUT WORDS : SUMS OF INTEGERS AS SUMS OF CUBES (1998) (0)
- Proof Without Words: Pythagorean Primes and Triangular Numbers (2019) (0)
- The derivative of the sine (2015) (0)
- The world's sneakiest substitution (2015) (0)
- The Relationship between Hyperbolic and Exponential Functions—Revisited (1992) (0)
- Proof Without Words: The Area of a Right Triangle (2007) (0)
- Tangent line inequalities (2015) (0)
- Problems and Solutions (2001) (0)
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