A. M. Mathai

A. M. Mathai

Often referred to as A. M. Mathai, Arakaparampil Mathai was a well-known Indian mathematician and astronomer who made significant contributions to the fields of reaction rate theory in astrophysics, special functions, and applied statistics. Mathai, who was born in Arakulam, Kerala, India, on April 28, 1935, has had a profound impact on the study of statistics, astronomy, and mathematics.

Early Life and Education

A. M. Mathai's academic career began with his outstanding performance at St. Thomas High School in Palai, Kerala, from which he graduated in 1953 with honors. He attended St. Thomas College in Palai to obtain his Bachelor of Science in Mathematics, which he completed in 1957. His academic aptitude was further demonstrated in 1959 when he graduated with a Master of Statistics in first class, first rank, and a gold medal from the University of Kerala.

Up until 1961, Mathai taught statistics at St. Thomas College in Palai, pursuing his love of the subject. His academic career took a global turn in 1961 when he was awarded the Canadian Commonwealth Scholarship. He was able to finish his master's degree in mathematics in 1962 and go on to get his doctorate in 1964 because of this grant.

Academic Career

After becoming an assistant professor at McGill University in Canada in 1964, Mathai's academic career continued there. His ascent through the ranks and his intellectual achievements ultimately resulted in his appointment as a full professor in 1979. Mathai worked at McGill University for a number of years, helping to shape the Department of Mathematics and Statistics until he retired in 2000 and was made an emeritus professor.

Teaching Experience

Mathai's journey in academia began as a Lecturer in Mathematics at St. Thomas College, Palai, University of Kerala, India, from 1959 to 1961. His dedication to teaching and research led him to Canada, where he served as an Assistant Professor at McGill University from 1964 to 1968. His academic stature grew, progressing to the position of Associate Professor (1968-1978) and subsequently Full Professor (1979-2000) at McGill University. Even in his emeritus role since 2000, Mathai continues to contribute to the academic community, combining his wealth of knowledge with a passion for teaching.

Contributions to Mathematics and Astrophysics

Mathai's contributions extend across a diverse array of mathematical and astrophysical disciplines. Notably, he established the Centre for Mathematical Sciences in Palai, Kerala, India, providing a platform for the advancement of mathematical research.

His prolific career includes the publication of over 25 books and more than 300 research papers. In recognition of his outstanding contributions, Mathai received the Founder Recognition Award from the Statistical Society of Canada in 1998. He is also honored as a Fellow of the National Academy of Sciences, India, and a Fellow of the Institute of Mathematical Statistics.

A. M. Mathai (Pioneer in Statistical Excellence)

In the world of statistics, A. M. Mathai stands as a towering figure, a luminary whose illustrious career has been marked by exceptional academic achievements, pioneering contributions, and a legacy of service to the global statistical community. From earning top honors in his academic pursuits to founding institutions that have shaped the field, Mathai's journey is a testament to his unwavering commitment to advancing the frontiers of statistical science.

Academic Triumphs

A. M. Mathai's journey into the realm of statistical brilliance began at the University of Kerala, where in 1959, he achieved an extraordinary feat by securing First Class, First Rank, and a Gold Medal in M. Sc (Statistics). This early academic success not only showcased Mathai's intellectual prowess but also set the tone for a career marked by excellence.

The pursuit of knowledge transcends boundaries, and Mathai's commitment to academic advancement led him to the prestigious Canadian Commonwealth Scholarship from 1961 to 1964. This scholarship not only recognized his exceptional abilities but also provided him with the platform to contribute to the global discourse on statistics.

Fellowships and Memberships

A. M. Mathai's influence in the field of statistics reached far beyond national borders. His recognition as a Fellow of the Institute of Mathematical Statistics in the United States solidified his place among the global statistical elite. Additionally, he was honored as a Fellow of the National Academy of Sciences in India, highlighting his significant contributions to the statistical landscape in his home country.

Mathai's impact on the international stage was further underscored by his election as a Member of the International Statistical Institute in The Netherlands. This prestigious membership not only acknowledged his achievements but also positioned him as a key figure in the global statistical community.

Founding Institutions

A. M. Mathai's dedication to the advancement of statistics is not confined to his achievements. He played a pivotal role in shaping the landscape of statistical research by founding crucial institutions. The establishment of The Canadian Journal of Statistics stands as a testament to his commitment to fostering a platform for scholarly discourse. Additionally, Mathai's founding of the Statistical Science Association of Canada, now the Statistical Society of Canada, has had a lasting impact on the development of statistical theory and practice in the country.

His contributions were further recognized with the Founder's Award from the Statistical Society of Canada, an acknowledgment of his visionary leadership and significant contributions to the statistical community.

Editorial and Review Contributions

Beyond his academic and institutional contributions, A. M. Mathai has played a crucial role in the dissemination of statistical knowledge through his editorial, review, and refereeing work. Serving as the Managing Editor and Editor of The Canadian Journal of Statistics and as a Regional Editor for Canada for the Statistical Theory and Methods Abstracts, Mathai has been instrumental in shaping the academic landscape.

His editorial responsibilities also extended to the Publications Series of the Centre for Mathematical Sciences in India, where he served as Editor for an array of publications ranging from books and proceedings of symposia to mathematical sciences for the general public.

A. M. Mathai's influence has reached far and wide, from special issues in the American Journal of Mathematical and Management Sciences to his membership on the editorial boards of prestigious journals such as Communications in Statistics, American Journal of Mathematical and Management Sciences, and International Journal of Mathematical and Statistical Sciences.

Selected Publications

Mathai's scholarly impact is evident in his selected publications, which span various mathematical and astrophysical domains. Some notable works include "An Introduction to Geometrical Probability: Distributional Aspects with Applications" (1999), "Jacobians of Matrix Transformations and Functions of Matrix Argument" (1997), and "Modern Problems in Nuclear and Neutrino Astrophysics" (co-authored with H.J. Haubold).

A. M. Mathai's research has significantly influenced the understanding of geometric probability, matrix trans quadratic forms, and gravitational instability in cosmology, among other topics.

No.TitlePublication DetailsCo-author(s)Year
1"Random p-content of a p-parallelotope in Euclidean n-space"Advances in Applied Probability, 31(2), 343-354-1999
2"An Introduction to Geometrical Probability: Distributional Aspects with Applications"Gordon and Breach, Newark-1999
3"Jacobians of Matrix Transformations and Functions of Matrix Argument"World Scientific Publishing, New York-1997
4"Appell's and Humbert's functions of matrix arguments"Linear Algebra and Its Applications, 183, 202-221-1993
5"On non-central generalized Laplacianness of quadratic forms in normal variables."Journal of Multivariate Analysis, 45, 239-246-1993
6"(With S.B. Provost) Quadratic Forms in Random Variables: Theory and Applications"Marcel Dekker, New YorkS.B. Provost1992
7"On a system of differential equations connected with the gravitational instability in a multi-component medium in Newtonian cosmology."Studies in Applied Mathematics, 80, 75-93-1989
8"(With H.J. Haubold) Modern Problems in Nuclear and Neutrino Astrophysics"Akademie-Verlag, BerlinH.J. Haubold-
9"On a conjecture in geometric probability regarding asymptotic normality of a random simplex."Annals of Probability, 10, 247-251-1982
10"(With R.S. Katiyar) Exact percentage points for testing independence."Biometrika, 66, 353-356R.S. Katiyar1979
11"(With P.N. Rathie) Recent contributions to axiomatic definitions of information and statistical measures through functional equations.."Essays in Probability and Statistics, Shinto, Tsusho, Tokyo, pp. 607-633P.N. Rathie1976
12"(With T.A. Davis) Constructing the sunflower head"Mathematical Biosciences, 20, 117-133T.A. Davis1974

Research Contributions

Mathai's research legacy is extensive and diverse, covering a wide array of mathematical and statistical domains. His notable research areas include:

Mathematical Statistics:

  • Statistical distribution theory
  • Multivariate analysis
  • Characterizations
  • Order statistics
  • Computational aspects (theory and numerical tables)
  • Quadratic forms
  • Bilinear forms
  • Matrix-variate distributions (real and complex cases)

Applied Statistics:

  • Design of experiments
  • Demography
  • Population models
  • Social statistics

Probability:

  • Geometrical probability
  • Queuing theory (limited to one paper)
  • Optimization (limited to one paper)

Astrophysics:

  • Reaction rates
  • Energy generation
  • Gravitational instability
  • Stellar models
  • Neutrino problems
  • Reaction-diffusion problems
  • Fractional calculus (recent work with physicists H.J. Haubold and R.K. Saxena)

Information Theory:

  • Characterization of Information Measures
  • Applications

Mathematics:

  • Generalized hypergeometric functions
  • G and H-funRandom.ctions
  • Functions of matrix argument
  • Graph theory (limited to one paper)
  • Functional equations (applications)
  • Integral equations
  • Differential equations (limited to two papers)
  • Statistical techniques applied to mathematics

Miscellaneous:

  • Biological models
  • Orthogonal polynomials
  • Dispersion theory
  • Axiomatization of basic statistical concepts
  • Pollution problems
  • Transportation problems

A Lifetime Dedicated to Statistical Advancement and Academic

A. M. Mathai's illustrious career in the field of mathematics and statistics spans decades, marked by a myriad of accomplishments, contributions, and leadership roles in various international professional societies. From his extensive involvement in organizing symposia to his role as a visiting full professor at prestigious institutions worldwide, Mathai's journey is a testament to his commitment to advancing statistical knowledge and fostering academic excellence.

International Professional Memberships and Reviewer Roles

Mathai's dedication to his field is evident through his memberships in esteemed organizations such as the Institute of Mathematical Statistics, International Statistical Institute, Canadian Statistical Society, and Environmetric Society. Despite facing financial constraints, he remained committed to these memberships, showcasing his unwavering passion for statistical research. His role as a reviewer for Mathematical Reviews and Zentralblatt für Mathematik further underscores his commitment to maintaining academic rigor and standards.

Organizing Symposia and Conferences

A significant aspect of Mathai's career is his role as the chief organizer of numerous national and international symposia, conferences, and schools. These events covered a broad spectrum of topics, ranging from functional equations to computer-oriented research in mathematical sciences. His contributions to areas like reliability and renewal theory, design of experiments, and distribution theory reflect the diversity of his expertise and interests.

Global Academic Engagement

Mathai's global influence extends beyond organizational roles. As an invited speaker, he participated in UN/ESA Workshops in various countries, including India, Egypt, Nigeria, Costa Rica, Germany, and Japan. His engagements as a speaker at international conferences worldwide, with recent appearances in Greece, Canada, Sicily, and India, highlight the global impact of his work and the recognition he has received from the international academic community.

Lecture Series and Visiting Professorships

Mathai's commitment to knowledge exchange is evident in his roles as an invited speaker for lecture series in Brazil, the United States, and Italy. His experiences as a visiting full professor at institutions such as the University of Texas at El Paso, the University of Campinas in Brazil, and the Indian Statistical Institute in Calcutta and Delhi demonstrate his dedication to fostering collaboration and sharing his expertise across borders.

Colloquium Speaker and Research Director

Having been an invited colloquium speaker in numerous countries, including Canada, the USA, Brazil, Greece, India, and Japan, Mathai's impact extends to diverse academic communities globally. His role as a research director under organizations like the Natural Sciences and the Engineering Research Council of Canada and the Department of Science and Technology in India underscores his significant contributions to advancing statistical research.

Academic Leadership and Mentorship

Mathai's influence extends to mentorship and academic leadership. Having supervised several Ph.D. and M.Sc. theses, his commitment to nurturing the next generation of statisticians is evident. As the director of SERC Schools in mathematical sciences, he played a crucial role in shaping the academic landscape for young faculty in India.

No.AuthorsTitleJournal/Proceedings/BookYear
1A.M. MathaiAn approximate analysis of a two-way layoutBiometrics1965
2A.M. Mathai and R.K. SaxenaOn a generalized hypergeometric distributionMetrika1966
3A.M. MathaiSampling distributions under missing valuesTrabajos de Estadistica1966
4A.M. MathaiPseudo-inverses in normal equationsStatistics1966
5A.M. MathaiSome characterizations of probability distributionsThe Canadian Mathematical Bulletin1966
6A.M. MathaiOn the multivariate exponential type distributionsJournal of the Indian Statistical Association1966
7A.M. MathaiOn a problem of regressionSouth African Journal of Statistics1967
8A.M. MathaiSome useful results in the analysis of dataTrabajos de Estadistica1967
9A.M. MathaiDispersion theoryStatistics1967
10A.M. MathaiDispersion and informationMetron1967
11A.M. MathaiOn the structural properties of conditional distributionsThe Canadian Mathematical Bulletin1967
12A.M. Mathai and R.K. SaxenaA short table of generalized hypergeometric distributionMetrika1968
13A.M. Mathai and R.K. SaxenaDistributions having gamma propertiesMetrika1968
14A.M. MathaiOrthogonal polynomials and a spectral decompositionJournal of the Indian Statistical Association1968
15A.M. MathaiSome limit theorems in terms of dispersionMetron1968
16H. Kaufman, A.M. Mathai, R.K. SaxenaRandom variables with random parametersSouth African Journal of Statistics1969
17A.M. Mathai and R.K. SaxenaApplications of special functions in the characterization of probability lawsSouth African Journal of Statistics1969
18A.M. Mathai and R.K. SaxenaDistribution of a product and structural setup of densitiesThe Annals of Mathematical Statistics1969
19A.M. Mathai and P.N. RathieThe exact distribution for the sphericity testJournal of Statistical Research1970
20A.M. Mathai and P.N. RathieAn expansion of G-function and its applications to statistical problemsRoy. Belg. Akad. Class des Sci.1970
21A.M. MathaiStatistical theory of distributions and Meijer's G-functionMetron1970
22A.M. Mathai and P.N. RathieThe exact distribution of Votaw's criterionAnnals of the Institute of Statistical Mathematics1970
23A.M. MathaiAn expansion of Meijer's G-function in the logarithmic case with applicationsMathematische Nachrichten1970
24A.M. MathaiThe exact distribution of Bartlett's criterionPubl. L'ISUP, Paris1970
25A.M. MathaiThe exact distribution of a criterion for testing the hypothesis that several multivariate populations are identicalJournal of the Indian Statistical Association1970
26A.M. Mathai and P.N. RathieThe problem of testing independenceStatistica1971
27A.M. Mathai and R.K. SaxenaExtension of Euler's integrals through statistical techniquesMathematische Nachrichten1971
28A.M. MathaiAn expansion of Meijer's G-function and the distribution of the product of independent beta variablesSouth African Journal of Statistics1971
29A.M. Mathai and P.N. RathieAn expansion of Wilks' generalized variance in the non-central linear caseSankhya Series A1971
30A.M. Mathai and P.N. RathieExact distribution of Wilks' criterionThe Annals of Mathematical Statistics1971
31A.M. MathaiOn the distribution of the likelihood ratio criterion for testing linear hypotheses on regression coefficientsAnnals of the Institute of Statistical Mathematics1971
32A.M. Mathai and R.K. SaxenaMeijer's G-function with matrix argumentActa Mexicana1971
33A.M. Mathai and R.K. SaxenaOn a generalized probability distributionUniv. Nac. Rev. Series A1972
34A.M. Mathai and R.K. SaxenaExpansion of Meijer's G-function of two variables when the upper parameters differ by integersKyungpook Mathematics Journal1972
35A.M. MathaiExact distribution of a criterion for testing equality of diagonal elements given that the covariance matrix is diagonal.Trabajos de Estadistica1972
36A.M. MathaiThe exact distribution of a criterion for testing the hypothesis that a covariance matrix is diagonalTrabajos de Estadistica1972
37H. Kaufman, A.M. Mathai, P.N. RathieA mathematical foundation for Pearson's chi-square goodness-of-fit statisticSankhya Series A1972
38A.M. MathaiA few remarks on the exact distribution of certain multivariate statisticsProceedings of the Symposium on Multivariate Analysis, Halifax1972
39A.M. MathaiProducts and ratios of generalized gamma variatesSkand. Aktuar.1972
40A.M. Mathai and P.N. RathieCharacterization of Matusita's measure of affinityAnnals of the Institute of Statistical Mathematics1972
41A.M. Mathai and P.N. RathieEnumeration of almost cubic mapsJournal of Combinatorial Theory1972
42A.M. MathaiThe exact distribution of three criteria associated with Wilks' concept of generalized varianceSankhya Series A1972
43A.M. MathaiThe exact non-central distribution of the generalized varianceAnnals of the Institute of Statistical Mathematics1972
44F.S. Gordon and A.M. MathaiCharacterization of multivariate normal distribution using regression propertiesThe Annals of Mathematical Statistics1972
45A.M. Mathai and R.K. SaxenaOn linear combinations of stochastic variablesMetrika1973
46A.M. Mathai and T.A. DavisA mathematical explanation of the emergence of foliar spirals in coconut and other palm treesProceedings of the National Science Academy (India)1973
47H. Kaufman and A.M. MathaiA mathematical foundation for the measure of affinityJournal of Multivariate Analysis1973
48A.M. MathaiA review of the various methods of obtaining the exact distributions of multivariate test criteriaSankhya Series A1973
49A.M. MathaiA few remarks on some recent articles on the exact distributions of multivariate test criteriaAnnals of the Institute of Statistical Mathematics1973
50A.M. Mathai and R.K. SaxenaGeneralized Hypergeometric Functions with Applications in Statistics and Physical SciencesSpringer-Verlag, Lectures Notes No.3481973
51A.M. Mathai and P.N. RathieCharacterizations of some statistical conceptsMeasures of Information and Their Applications, IIT, Bombay1974
52Aleyamma George and A.M. MathaiApplications of the concepts of affinity and distance to population problemsJournal of Biosocial Sciences (London)1974
53T.A. Davis and A.M. MathaiConstructing a sunflower headMathematical Biosciences1974
54Aleyamma George and A.M. MathaiDistributions of inter-live-birth intervalsSankhya Series B1975
55A.M. MathaiBounds for moments through a general orthogonal expansion in a pre-Hilbert space-IThe Canadian Journal of Statistics1975
56Aleyamma George and A.M. MathaiA measure of group behaviour, its characterization, and applications in socio-anthropological studiesCanadian Studies in Population1975
57A.M. Mathai and P.N. RathieBasic Concepts in Information Theory and Statistics: Axiomatic Foundations and ApplicationsWiley Halsted, New York and Wiley Eastern, New Delhi1977
58A.M. Mathai and P.N. RathieRecent contributions to axiomatic definitions of information and statistical measures through functional equationsEssays in Probability and Statistics1976
59Aleyamma George and A.M. MathaiDistribution of birth interval based on original dataDemography of India1976
60A.M. MathaiBounds for moments through a general orthogonal expansion in a pre-Hilbert space -IIThe Canadian Journal of Statistics1976
61A.M. Mathai and P.N. RathieProbability and StatisticsMacmillan and Co, London and New Delhi1977
62A.M. MathaiAn axiomatic foundation for the multivariate measure of affinity with applications in social statisticsTransactions of the Seventh Prague Conference on Information Theory1977
63A.M. Mathai and W.Y. TanThe non-null distribution of the likelihood ratio criterion for testing the hypothesis that the covariance matrix is diagonalThe Canadian Journal of Statistics1977
64A.M. MathaiA short note on the non-null distribution for the problem of sphericitySankhya Series B1978
65A.M. Mathai and G. PederzoliCharacterization of the Normal Probability LawWiley Halsted, New York and Wiley Eastern, New Delhi1977
66A.M. MathaiA new approach to multivariate statistical distributionsProceedings of the 11th Brazilian Mathematical Colloquium1978
67A.M. Mathai and R.K. SaxenaThe H-function with Applications in Statistics and Other DisciplinesWiley Halsted, New York and Wiley Eastern, New Delhi1978
68Aleyamma George and A.M. MathaiA study of live births and group behaviour by using a measure of attractionThe Manpower Journal1978
69A.M. MathaiOn the non-null distribution of Wilks' LmvcSankhya Series B1978
70A.M. MathaiSome results on functions of matrix argumentMathematische Nachrichten1978
71A.M. Mathai and R.K. SaxenaFox's H-function with matrix argumentJournal de Matematica e Estatistica1979
72A.M. MathaiThe exact distribution and the exact percentage points for testing equality of variances in independent normal populationJournal of Statistical Computations and Simulation1979

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