Donald St. P. Richards

Born:

place: West Indies

B.Sc. Mathematics-Special Honors University of the West Indies, 1976

Ph.D. University of the West Indies 1978
thesis: The Exact Distributions of a Class of Likelihood Ratio CTest Statistics; Advisor: Rameshwar Gupta

Professor of Statistics, Pennsylvania State University

URL: http://www.stat.virginia.edu/richards.html
E-Mail: drichards@virginia.edu
email:

In two years, Donald Richards went from an undergraduate degree to a Ph.D. (Mathematical Statistics, University of the West Indies, 1978). While pubishing numerous papers, he had several positions: University of the West Indies (1979-1981); University of North Carolina (1981-1987); University of Wyoming (1983-1984). In 1987 he joined the Statstics faculty of the University of Virginia, Charlottesville. Currently and since 1994, Dr. Richards is Chair of the Division of Statistics of the University of Virginia

Dr. Richards has had four Ph.D. students.

Selected Committee Memberships

Committee on Doctoral and Postdoctoral Study in the United States, National Research Council, 1990-1991
Board on Mathematical Sciences, 1993-1999
U.S. Delegation to the International Mathematical Union, Lucerne, Switzerland, 1994
School Improvement Program Committee, Greer Elementary School, Charlottesville, VA, 1995-1997

Research

Area Interests: Multivariate statistical analysis, Representation theory and harmonic analysis, Generalized special functions, Statistical reliability theory, Probability inequalities.

In multivariate statistical analysis, studying parametric and semi-parametric probability distributions and their properties, with applications to multivariate inferential problems such as hypothesis testing and discriminant analysis.

In generalized special functions, a program of research to investigate hypergeometric functions defined on
matrix spaces and symmetric cones. This program is motivated by applications to problems in multivariate analysis.

The research on generalized special functions has led also to generalizations of results well-known for the classical special functions; this line of work relies heavily on representation theory and harmonic analysis.

The algebraic and analytic techniques utilized in my work on multivariate analysis and generalized special functions are closely related to my research on total positivity and probability inequalities, e.g. new concepts of total positivity germane to the theory of finite reflection groups, and correlation inequalities of FKG type, motivated by problems in statistics, probability and mathematical physics.

BOOKS

Edited: Donald St. P. Richards. Hypergeometric functions on domains of positivity, Jack polynomials, and applications. Proceedings of the AMS Special Session held in Tampa, Florida, March 22--23, 1991. Contemporary Mathematics, 138. American Mathematical Society, Providence, RI, 1992. x+259 pp. ISBN: 0-8218-5159-4

Edited: Tuong Ton-That, Kenneth I. Gross, Donald St. P. Richards and Paul J. Sally, Jr. Representation theory and harmonic analysis. Papers from the conference held in honor of Ray A. Kunze at the AMS Special Session, Cincinnati, Ohio, January 12--14, 1994. Contemporary Mathematics, 191. American Mathematical Society, Providence, RI, 1995. xii+254 pp. ISBN: 0-8218-0310-7

Papers Published

Dr. Donald St. P. Richards has published over 50 papers in Mathematical Analysis and Statistics

50. Gross, Kenneth I.; Richards, Donald St. P. Algebraic methods toward higher-order probability inequalities. Stochastic processes and related topics, 185--206, Trends Math., Birkhäuser Boston, Boston, MA, 1998.

49. Garren, Steven T.; Richards, Donald St. P. General conditions for comparing the reliability functions of systems of components sharing a common environment. J. Appl. Probab. 35 (1998), no. 1, 124--135.

48. Gupta, Rameshwar D.; Richards, Donald St. P. Invariance properties of some classical tests for exponentiality. J. Statist. Plann. Inference 63 (1997), no. 2, 203--213.

47. Gupta, Rameshwar D.; Richards, Donald St. P. Multivariate Liouville distributions. V. Advances in the theory and practice of statistics , 377--396, Wiley Ser. Probab. Statist. Appl. Probab. Statist., Wiley, New York, 1997.

46. Woodham, Sara-Anne; Richards, Donald St. P. Comparison of system reliability functions under laboratory and common operating environments. J. Appl. Probab. 34 (1997), no. 2, 536--545.

45. Richards, Donald St. P. New classes of probability inequalities for some classical distributions. Multidimensional statistical analysis and theory of random matrices (Bowling Green, OH, 1996), 217--224, VSP, Utrecht, 1996.

44. Ding, Hongming; Gross, Kenneth I.; Richards, Donald St. P. Ramanujan's master theorem for symmetric cones. Pacific J. Math. 175 (1996), no. 2, 447--490.

43. Richards, Donald St. P.; Gross, Kenneth I. Total positivity, harmonic analysis and random walks on Weyl chambers. Representation theory and harmonic analysis (Cincinnati, OH, 1994), 153--161, Contemp. Math., 191, Amer. Math. Soc., Providence, RI, 1995.

42. Gupta, Rameshwar D.; Misiewicz, Jolanta K.; Richards, Donald St. P. Infinite sequences with sign-symmetric Liouville distributions. Probab. Math. Statist. 16 (1996), no. 1, 29--44.

41. Richards, Donald St. P. Exact asymptotics for some probability distributions on compact manifolds. Ann. Statist. 23 (1995), no. 5, 1582--1586.

40. Lu, I-Li; Richards, Donald Total positivity properties of the bivariate diagonal natural exponential families. Statist. Probab. Lett. 26 (1996), no. 2, 119--124.

39. Gupta, Rameshwar D.; Richards, Donald St. P. Multivariate Liouville distributions. IV. J. Multivariate Anal. 54 (1995), no. 1, 1--17.

38. Gross, Kenneth I.; Richards, Donald St. P. Total positivity, finite reflection groups, and a formula of Harish-Chandra. J. Approx. Theory 82 (1995), no. 1, 60--87.

37. Bar-Lev, Shaul K.; Bshouty, Daoud; Enis, Peter; Letac, Gérard; Lu, I-Li; Richards, Donald The diagonal multivariate natural exponential families and their classification. J. Theoret. Probab. 7 (1994), no. 4, 883--929.

36. Misiewicz, Jolanta K.; Richards, Donald St. P. Positivity of integrals of Bessel functions. SIAM J. Math. Anal. 25 (1994), no. 2, 596--601.

35. Lu, I-Li; Richards, Donald Random discriminants. Ann. Statist. 21 (1993), no. 4, 1982--2000.

34. Gross, Kenneth I.; Richards, Donald St. P. Constant term identities and hypergeometric functions on spaces of Hermitian matrices. J. Statist. Plann. Inference 34 (1993), no. 1, 151--158.

33. Gupta, Rameshwar D.; Richards, Donald St. P. Multivariate Liouville distributions. III. J. Multivariate Anal. 43 (1992), no. 1, 29--57.

32. Gupta, Rameshwar D.; Richards, Donald St. P. Multivariate Liouville distributions. II. Probab. Math. Statist. 12 (1991), no. 2, 291--309 (1992).

31. Bingham, Christopher; Chang, Ted; Richards, Donald Approximating the matrix Fisher and Bingham distributions: applications to spherical regression and Procrustes analysis. J. Multivariate Anal. 41 (1992), no. 2, 314--337.

30. Peddada, Shyamal Das; Richards, Donald St. P. Entropy inequalities for some multivariate distributions. J. Multivariate Anal. 39 (1991), no. 1, 202--208.

29. Peddada, Shyamal D.; Richards, Donald St. P. Acknowledgment of priority: "Proof of a conjecture of M. L. Eaton on the characteristic function of the Wishart distribution" [Ann. Probab. 19 (1991), no. 2, 868--874]. Ann. Probab. 20 (1992), no. 2, 1107.

28. Peddada, Shyamal Das; Richards, Donald St. P. Proof of a conjecture of M. L. Eaton on the characteristic function of the Wishart distribution. Ann. Probab. 19 (1991), no. 2, 868--874.

27. Gross, Kenneth I.; Richards, Donald St. P. Hypergeometric functions on complex matrix space. Bull. Amer. Math. Soc. (N.S.) 24 (1991), no. 2, 349--355.

26. Richards, Donald St. P. Totally positive kernels, Pólya frequency functions, and generalized hypergeometric series. Linear Algebra Appl. 137/138 (1990), 467--478.

25. Gross, Kenneth I.; Richards, Donald St. P. Total positivity, spherical series, and hypergeometric functions of matrix argument. J. Approx. Theory 59 (1989), no. 2, 224--246.

24. Askey, Richard; Richards, Donald Selberg's second beta integral and an integral of Mehta. Probability, statistics, and mathematics, 27--39, Academic Press, Boston, MA, 1989.

23. Gupta, Rameshwar D.; Richards, Donald St. P. The Dirichlet distributions and polynomial regression. J. Multivariate Anal. 32 (1990), no. 1, 95--102.

22. Richards, Donald St. P. The central limit theorem on spaces of positive definite matrices. J. Multivariate Anal. 29 (1989), no. 2, 326--332.

21. Richards, Donald St. P. Analogs and extensions of Selberg's integral. $q$-series and partitions (Minneapolis, MN, 1988), 109--137, IMA Vol. Math. Appl., 18, Springer, New York-Berlin, 1989.

20. Richards, Donald St. P. Constant regression polynomials and the Wishart distribution. SIAM J. Math. Anal. 20 (1989), no. 2, 504--510.

19. Gupta, Rameshwar D.; Richards, Donald St. P. Multivariate Liouville distributions. J. Multivariate Anal. 23 (1987), no. 2, 233--256.

18. Gross, Kenneth I.; Richards, Donald St. P. Special functions of matrix argument. I. Algebraic induction, zonal polynomials, and hypergeometric functions. Trans. Amer. Math. Soc. 301 (1987), no. 2, 781--811.

17. Gross, Kenneth I.; Richards, Donald St. P. Compact group actions, spherical Bessel functions, and invariant random variables. J. Multivariate Anal. 21 (1987), no. 1, 128--138.

16. Richards, Donald St. P. Positive definite symmetric functions on finite-dimensional spaces. II. Statist. Probab. Lett. 3 (1985), no. 6, 325--329.

15. Richards, Donald St. P. Positive definite symmetric functions on finite-dimensional spaces. I. Applications of the Radon transform. J. Multivariate Anal. 19 (1986), no. 2, 280--298.

14. Richards, Donald St. P.; Gupta, Rameshwar D. Letter values in multivariate exploratory data analysis. The merging of disciplines: new directions in pure, applied, and computational mathematics (Laramie, Wyo., 1985), 175--183, Springer, New York-Berlin, 1986.

13. Richards, Donald St. P. Applications of invariant differential operators to multivariate distribution theory. SIAM J. Appl. Math. 45 (1985), no. 2, 280--288.

12. Gupta, Rameshwar; Richards, Donald Testing optimality of experimental designs for a regression model with random variables. J. Statist. Plann. Inference 11 (1985), no. 1, 75--80.

11. Richards, Donald Hyperspherical models, fractional derivatives and exponential distributions on matrix spaces. Sankhy\=a Ser. A 46 (1984), no. 2, 155--165.

10. Gupta, Rameshwar D.; Richards, Donald St. P. Hypergeometric functions of scalar matrix argument are expressible in terms of classical hypergeometric functions. SIAM J. Math. Anal. 16 (1985), no. 4, 852--858.

9. Gupta, Rameshwar D.; Richards, Donald St. P. Application of results of Kotz, Johnson and Boyd to the null distribution of Wilks' criterion. Contributions to statistics, 205--210, North-Holland, Amsterdam-New York, 1983.

8. Richards, Donald Representations for eigenfunctions of expected value operators in the Wishart distribution. Statist. Probab. Lett. 1 (1983), no. 3, 141--145.

7. Gupta, Rameshwar D.; Richards, Donald St. P. Series expansion for a hypergeometric function of matrix argument with applications. Austral. J. Statist. 24 (1982), no. 2, 216--220.

6. Richards, Donald St. P. Differential operators associated with zonal polynomials. I, II. Ann. Inst. Statist. Math. 34 (1982), no. 1, 111--117, 119--121.

5. Richards, Donald St. P. Stability theorems for some characterizations of the exponential distribution. Ann. Inst. Statist. Math. 33 (1981), no. 2, 199--204.

4. Richards, Donald St. P. A characterization of a matric-variate exponential distribution. Austral. J. Statist. 23 (1981), no. 2, 238--239.

3. Richards, Donald; Gupta, Rameshwar D. The exact distribution of Wilks' criterion. South African Statist. J. 13 (1979), no. 1, 7--14.

2. Gupta, Rameshwar D.; Richards, Donald Calculation of zonal polynomials of $3\times 3$ positive definite symmetric matrices. Ann. Inst. Statist. Math. 31 (1979), no. 2, 207--213.

1. Gupta, Rameshwar D.; Richards, Donald Exact distributions of Wilks' $\Lambda$ under the null and nonnull (linear) hypotheses. Statistica (Bologna) 39 (1979), no. 2, 333--342.

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