C.R.Rao Advanced Institute of Mathematics, Statistics and Computer Science (AIMSCS)

University of Hyderabad Campus, Gachibowli, Hyderabad – 500 046


C.R. Rao was born on 10 September 1920 in Huvanna Hadagali, now in Karnataka State. He studied in schools at Gudur, Nuzvid, Nandigama, and Visakhapatnam, in Andhra Pradesh and completed his M.A. degree in Mathematics at the Andhra University in Waltair, Andhra Pradesh. He did his M.A. degree in Statistics from Calcutta University in Kolkata, West Bengal.

C.R. Rao worked in India at the Indian Statistical Institute for 40 years before he took mandatory retirement at the age of 60. He moved to the USA and worked for another 25 years at the University of Pittsburgh and the Pennsylvania State University. In reply to a query put to him as to what particular achievement he is most proud of, C.R. Rao replied, “it is the outstanding contributions my students are making to statistical theory and practice.”


Prof. Rao in Cambridge

Professor C.R Rao Academic Life:

  • He studied in schools at Gudur, Nuzvid, Nandigama, and Visakhapatnam, in Andhra Pradesh
  • MA degree in Statistics from Calcutta University with a first-class, first rank and a record of marks unbeaten till now, and a gold medal (1943).
  • Rao received an MA degree in Mathematics with a first-class and first rank from Andhra University (1941)

Research Career of Prof. C.R. Rao:

  • He was invited to work on a project at the Museum of Anthropology and Archeology at Cambridge University, UK, which required the Statistical Methodology developed by P.C. Mahalanobis, the founder of ISI.
  • Based on the work he did, he earned his Ph.D. in 1948 from Cambridge University with R.A. Fisher.
  • C.R. Rao worked in India at the Indian Statistical Institute for 40 years (1941-79)
  • He moved to the USA and worked for another 25 years at the University of Pittsburgh and the Pennsylvania State University.

Prof. C. R. Rao and Prof.Roy Frieden at the University of Texas in 2010 during Rao’s 90th birthday celebrations.


  • Indian Statistical Institute, in various capacities 1941-1979
  • Visiting Professor at University of Illinois 1951-1952
  • National Professor of India 1987-1992
  • University Professor, University of Pittsburgh 1979-1988
  • Eberly Professor of Statistics
  • The Pennsylvania State University (PSU), PA, USA 1988-2001
  • Eberly Professor Emeritus (PSU) 2001
  • Director, Centre for Multivariate Analysis, PSU 2001-2010
  • Indian Statistical Institute, in various capacities 1941-1979
  • Visiting Professor at University of Illinois 1951-1952
  • National Professor of India 1987-1992
  • University Professor, University of Pittsburgh 1979-1988
  • Eberly Professor of Statistics,
  • The Pennsylvania State University (PSU), PA, USA 1988-2001
  • Eberly Professor Emeritus (PSU) 2001
  • Director, Centre for Multivariate Analysis, PSU 2001-2010

Research Professor, University at Buffalo, SUNY 2010 - Retired from active service at the age of 80 from The Pennsylvania State University, PA, USA and continues to hold honorary Professorship at The Pennsylvania State University, PA, USA and at the University at Buffalo, SUNY, USA.


As Head and later Director of the Research and Training School at the ISI for a period of over 40 years, Rao developed research and training programs and produced outstanding students which “put India not far from the center of the statistical map of the world”, and earned for ISI the name of Indian School of Statistics. During this period he also directed the training programs at the International Statistical Educational Center which led to the development of statistics in the South East Asian region. Rao was the Chairman of a UN Committee, which examined the demand for statistical personnel in Asian countries and recommended the establishment of an Institute for statistical development in South East Asia. On the basis of his recommendation The Asian Statistical Institute now known as Statistical Institute for Asia and Pacific was established in Tokyo to provide training to statisticians working in government and industrial organizations.

C.R. Rao played an important role, under the direction the doyen of Indian statistics, P.C. Mahalanobis, in setting up state statistical bureaus in different states of India and developing a network of statistical agencies at the district level for collection of data. Together with the Central Statistical Organization and the National Sample Survey in planning of which, C.R. Rao played a significant role, India has one of the best national statistical systems. He founded the Indian Econometric Society, which has been active in promoting quantitative studies in economics for planning purposes.

C.R. Rao was the founder of Indian Econometric Society and Indian Society for Medical Statistics which hold conferences every year to discuss problems of current interest.


After taking compulsory retirement in India at the age of 60 with 40 years of service at ISI, Rao tried to get a suitable job in India to continue his research activities without administrative responsibilities. As opportunities to work in India were denied, he accepted unsolicited offers of distinguished professorships in USA.

He worked for another 25 years as University Professor at the University of Pittsburgh and Eberly (Chair) Professor of Statistics at The Pennsylvania State University continuing his research in diverse areas of statistics. He retired from active service at the age of 81 but continued his research activities as Eberly Professor Emeritus and Director of the Center for Multivariate Analysis at The Pennsylvania State University. In 2010, he moved to Buffalo accepting Research Professorship at the University at Buffalo. He published 201 research papers during his 40 years stay in India and 272 research papers during his 30 years of stay in USA.


C. Radhakrishna Rao is among the world leaders in statistical science over the last six decades. His research, scholarship, and professional services have had a profound influence on theory and applications of statistics.

Technical terms such as, Cramer-Rao inequality, Rao-Blackwellization, Rao’s Score Test, Fisher-Rao and Rao Theorems on second order efficiency of an estimator, Rao

metric and distance, Analysis of Dispersion (MANOVA) and Canonical Variate analysis and G-inverse of matrices appear in all standard books on statistics. Cramer-Rao Bound and Rao-Blackwellization are the most frequently quoted key words in statistical and engineering literature. Special uses of Cramer-Rao Bound under the technical term, Quantum Cramer- Rao Bound have appeared in Quantum Physics. Rao-Blackwellization has found applications in adaptive sampling, particle filtering in high-dimensional state spaces, dynamic Bayesian networks etc. These results have led to contributions of strategic significance to signal detection, tracking of non-friendly planes and recognition of objects by shape.

Other technical terms bearing his name appearing in specialized books are Rao’s F and U tests in multivariate analysis, Rao’s Quadratic Entropy, Cross Entropy and Rao-Rubin, Lau-Rao, Lau-Rao-Shanbhag and Kagan-Linnik-Rao theorems on characterization of probability distributions. Two of his papers, one on estimation leading to many technical terms and key words and another on score test which had a high impact on the development of statistical theory appear in the book Breakthroughs in Statistics: 1889-1990.

Rao has made some significant contributions to combinatorial mathematics for use in design of experiments, the most important of which is Orthogonal arrays (OA).The basic paper on the subject appeared in Proc. Edinburgh Math. Soc. (the referee of the paper reported that it is a fresh and original piece of work). The Japanese Quality Control Expert, G.Taguchi made extensive use of OA’s (described by Forbes Magazine as “new mantra” for industries), in industrial experimentation.

Rao defined a generalized inverse (g-inverse) of a matrix (singular or rectangular) and demonstrated its usefulness in the study of linear models and singular multivariate normal distributions.

He is the author of 14 books and about 350 research papers. Three of his books have been translated into several European and Chinese and Japanese languages.


C.R. Rao is the eighth child in a family of six brothers and four sisters who were raised by his parents, C.D. Naidu and Lakshmikantamma, and was named Radhakrishna following the tradition of naming the eighth child in a family after God Krishna, who is the eighth child. He married Bhargavi who has two master’s degrees, one from Banaras Hindu University in History and another from the University of Illinois, USA, in Psychology, and a Bachelor’s degree in Teacher’s Training. She worked as a professor of psychology at Jadavpur University, Kolkata for a number of years.

They have a daughter, Tejaswini who holds a Ph.D. in Nutrition from the Pennsylvania State University and works as a Professor in the Dietetics and Nutrition department at the SUNY College, Buffalo. She is an accomplished dancer of the Bharatanatyam and Kuchipudi classical dance styles and is the director of a dance school called Natya.

They have a son, Veerendra who is an electrical engineer and computer scientist. He has a computer consultancy in Pittsburgh. He has two sons, Amar and Rohith.


  • Amari, a renowned mathematician from Japan:
    Dr. Rao is a great scholar beyond the framework of statistics, which he himself has founded. It is a big surprise to see that his influence has been effective and has played a great role for more than half a century to produce fruitful developments in several scientific disciplines. “The idea of connecting statistics and differential geometry was too early at that time (1945). However, after nearly half a century, Rao’s idea has been developed to become one of most active and important topics in information sciences, connecting statistics, information theory, control and statistical physics.”
  • In an article entitled “The Statistical Century” published in the Royal Statistical Society News (Vol 22, Jan 1995), the Distinguished American Statistician Bradley Efron stated:
    Karl Pearson’s famous chi-square paper appeared in the spring of 1900, an auspicious beginning to a wonderful century for the field of statistics. The first half of the century was the golden age of statistical theory, during which our field grew from ad hoc origins, similar to the current state of computer science, into a firmly grounded mathematical science. Men of the intellectual calibre of Fisher, Neyman, Pearson, Hotelling, Wald, Cramer and Rao were needed to bring statistical theory to maturity
  • A review of C.R. Rao’s book, Linear Statistical Inference and its Applications, by the famous statistician, W.G. Cochran in the Journal of the Franklin Institute states the following:
    R. Rao would be found in almost any statistician’s list of the five outstanding workers in the world of Mathematical Statistics today. His book represents a comprehensive account of the main body of results that comprise modern statistics theory.
  • Efron, President of the American Statistical Association, mentions in the Issue 327, September 2004, of AMSTAT while introducing the article by C.R. Rao on Reflections on the past and visions for the future:
    C.R. Rao, Eberly Professor Emeritus in the Statistics Department at Penn State is a towering figure in the postwar development of statistical theory. Among his great many honors, he was recently awarded the National Medal of Science, the government’s highest scientific prize.
  • Karlin, mathematician who won President’s medal:
    C.R. Rao is among the worldwide leaders in statistical science over the last five decades. His research, scholarship, and professional service have had a profound influence in the theory and applications of statistics and are incorporated into standard references for statistical study and practice.C.R. Rao is not only a highly creative theoretician, but was attracted and labored with many data sets in health, biology, psychology, and social sciences.
  • Citation while awarding Hon. D.Sc. by the Ohio State University
    Among the international community of scholars, you are widely acknowledged as one of the world’s foremost statisticians. In the complex realms of statistics and higher mathematics, your research and scholarly writing have opened new doors of understanding. The statistical theories and applications, which bear your name, attest to the fundamental contributions you have made to your field and to the larger body of man’s knowledge. Numerous honors and awards have followed, in tribute to an unusually distinguished and productive life of inquiry. You have earned the highest accolade of all, the esteem of your peers throughout the world of scholarship.
  • Press release by Government of India on appointment as National Professor (limited to 12 at any time)
    Government has appointed C.R. Rao, an eminent statistician, as National Professor. Professor Rao is an outstanding and creative thinker in the field. He was appointed by Professor Mahalanobis as full-fledged professor of the Indian Statistical Institute at the early age of 29 in recognition of his creativity.
  • The Institute of Combinatorial Mathematics and its Applications elected C.R. Rao as an Honorary Member with the citation:
    …as the world’s leading expert in statistical design theory.
  • Armitage, Professor of Statistics, Oxford University, UK, writes in a review of Statistical Analysis and Inference (Ed. Y. Dodge):
    C. Radhakrishna Rao is a polymath amongst statisticians. …Rao’s research interests include social, industrial and economic applications. He has been (and still is) an influential teacher especially in third world countries. …The group of papers are interspersed with quatrains from Rubaiyat of Omar Khayyam of Naishapur, whose hedonistic nihilism seems to accord ill with C.R. Rao’s outlook:” Myself when young did eagerly frequent/ Doctor and Saint ,and heard great Argument/ About it and about: but evermore/ came out by the same door as I went”. Those of us who have frequented C.R.’s company have invariably found new doors open.
  • A. Fisher in a speech at the Indian Statistical Institute on February 12, 1963:
    For its (ISI) educational programs, the institute needs not only leaders of mathematical thought like Professor Rao, who can uphold and maintain the high place in the world opinion that Indians have already won