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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