# Samarendra Nath Roy

### Born: 11 December 1906 in Calcutta, (now Kolkata) India

Died: 23 July 1964 in Jasper, Canada

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**Samarendra Nath Roy**'s parents were Suniti Bala and Kali Nath Roy who was the editor of

*The Tribune*, a nationalist daily newspaper published in Lahore. Samarendra Nath was the oldest of his parents two children. A major incident occurred in April 1919 when the British massacred Indians at Jalianwala Baag.

*The Tribune*published a news report,

*Prayer at the Jama Masjid*, on 6 April 1919. Kali Nath Roy was brought before the Martial Tribunal under Lieutenant Colonel Irvine and was sentenced to rigorous imprisonment for two years and a fine of Rs 1,000. All this occurred while Samarendra Nath was studying at the Khulna District School. He graduated in the first division in the Matriculation Examination of 1923 and entered the Daulatpur Hindu Academy later that year. The Academy was situated in Khulna and had been affiliated to the University of Calcutta since 1914. He was ranked first in the Intermediate Science (Higher Secondary) Examinations from the Academy in 1925. Then, remaining in the University of Calcutta, he moved to Presidency College Kolkata. He obtained a B.Sc. Mathematics (Honours) in 1928, being ranked first in the list of First Class students. He continued to study for a Master's Degree and was awarded an M.Sc. in 1931 having submitted a dissertation on the

*Theory of Relativity*.

After completing work for his Master's Degree, Roy was appointed as a Research Associate in the Applied Mathematics Department of Calcutta University to work on cosmology with N R Sen. This work led to partial differential equations which could only be solved numerically, but at this time the Applied Mathematics Department had no computing facilities. Roy was allowed to use the computing facilities in the Indian Statistical Institute, which were the only such facilities available in Calcutta. The Institute was run by P C Mahalanobis and soon Roy became interested, not only in solving his cosmological problems, but also in the statistical work of the Institute. He joined the Institute in 1934 on a part-time basis, then became a full-time member in the following year.

In the Indian Statistical Institute he quickly moved to become the leader of a group of talented young statisticians such as Raj Chandra Bose, K R Nair, K Kishen, C R Rao, J M Sengupta and H C Sinha. He made important contributions to multivariate analysis, working on his own and also collaborating with other members of the group. There was no Department of Statistics in the University of Calcutta at this time so, in 1938, while continuing to undertake research in the Statistical Institute, he was appointed as a lecturer in the Applied Mathematics Department. Three years later, after the Statistics Department had been set up, he transferred from Applied Mathematics to Statistics and, together with Prasanta Chandra Mahalanobis and Raj Chandra Bose, set up the course structure and content. Roy soon gained important positions within the Statistical Institute and the Statistics Department, being assistant director of the former from 1946 to 1949 and acting Head of the Statistics Department during 1947-48. A sample of the papers Roy published during this period follows:

*The use and distribution of the Studentized D*

^{2}

*-statistic when the variances and covariances are based on k samples*(1940),

*On hierarchical sampling, hierarchical variances and their connexion with other aspects of statistical theory*(1940),

*The distribution of the root-mean-square of the second type of the multiple correlation co-efficient*(1940),

*Analysis of variance for multivariate normal populations: the sampling distribution of the requisite p-statistics on the null and non-null hypotheses*(1942),

*Bernoulli's theorem and Tshebycheff's analogue*(1945),

*On a certain class of multiple integrals*(1945),

*Notes on testing of composite hypotheses*(1947), and

*On the construction of an unbiassed and most powerful critical region out of any given statistic*(1948).

Roy travelled to the United States in the spring of 1949 to take up a Visiting Professorship of Statistics at Columbia University in New York. He returned to India for the beginning of the academic year 1949-50 and became Head of the Department of Statistics in the University of Calcutta. However, in the spring of 1950 he returned to the United States to take up a position as a full professor in the Statistics Department of the University of North Carolina. He published

*Some aspects of multivariate analysis*in 1957, a book which brought together many of the ideas Roy had published. S Kullback writes:-

G S Mudholkar, who was Roy's final doctoral student, writes [5]:-This monograph does not attempt to cover the entire area of multivariate analysis, the statistical analysis of samples from multivariate normal populations, or even a major part of it. The monograph deals with samples of fixed size, and the main emphasis is on obtaining confidence bounds on certain parametric functions that are a set of natural measures of deviation from a null hypothesis. The first twelve chapters lead up to the confidence bounds which are discussed in detail in chapters13and14. In chapter15, the last of the monograph, some nonparametric generalizations of analysis of variance and multivariate analysis applied to categorized data in contingency tables are considered ...

In [1], his colleague Raj Chandra Bose writes:-Roy was a courteous, gentle and modest person who was admired and respected by all who knew him. He was an inspiring, caring teacher always thoughtful of his students' concerns and feelings. He was a creative and original yet low-key and self-effacing scholar who gave academic help to anyone who needed it. As a thesis advisor he was demanding yet generous and responsible. He was always mindful of the personal conditions and problems of his students. In the words of his doctoral student Yashwant Sathe, he emphasized the "fundamentals of the subject" and "treated all his Ph.D. students on equal footing and as his family members". In a recent communication, Dr Sathe recalled his caring nature by describing Roy's1962visit to Pune, India, when I, Mudholkar, was in the final stage of my thesis. Roy made it his duty to visit my family to tell them of my progress and to reassure them of my well-being and a reasonable future. Another of his doctoral students, Ram Gnanadesikan ... has observed that his "rare and genuine modesty was as exemplary as his quiet intellectual timber was exciting". He continues further, "As the Bard of Avon so aptly said it:

His life was gentle, and the elements

So mixed in him that Nature might stand up

And say to all world, "This was a man".

Indeed, looking back on his life and work it is easy to see that he made unusual contributions to statistics and therefore to science and consequently to well-being of all.

Jagdish N Srivastava writes in [8]:-Roy was one of the most self-effacing of men. To his students and to his numerous friends and relatives he gave of his best without any regard for his own convenience. He had a keen sense of humour and a warm friendly personality. He was a stimulating colleague and a dedicated teacher-scholar in the best academic tradition. He was a devoted husband and loving father ...

Roy received many honours for his outstanding contributions. He was elected a Fellow of the National Institute of Sciences in India in 1946, a Fellow of the International Statistical Institute in 1951. He was President of the Statistical Section of the Indian Science Congress in 1948. He was a Fellow of the Institute of Mathematical Statistics. In 1970 the bookProfessor S N Roy was not just one man; he was a procession of men. He was a profound and fundamental thinker and researcher in many wide fields of Statistics. He was not only a good father and husband, but also very fatherly to the students. Exceptionally compassionate, he went into great details of the day to day problems, difficulties, health concerns, and the joys and sorrows of his students, and offered them generous advice and help. He occasionally invited them to his home for dinner, where they were treated as if they were with their own parents. He was very informal. He was a man who practised simple living and high thinking. He was above favouritism and narrow-mindedness. He believed that every human being deserved to live in freedom and dignity. He had a great vision for the world including India where he was born. That vision, with respect to which he was awake and which he carefully practised in his life, can be aptly summarized by the poem of Tagore(Nobel Prize,1913):

Where the mind is without fear and the head is held high

Where knowledge is free

Where words come out of the depth of truth

Where tireless striving stretches its arms towards perfection

Where the clear stream of reason has not lost its way into the dreary desert sand of dead habit

Where the mind is led forward by Thee into ever widening thought and action

Into that heaven of freedom, my Father, let my country awake.

*Essays in probability and statistics*, edited by R C Bose, I M Chakravarti, P C Mahalanobis, C R Rao and K J C Smith, dedicated to his memory was published in the University of North Carolina Monograph Series in Probability and Statistics. In 2007 a special issue of the

*Journal of Statistical Planning and Inference*was published in celebration of the centennial of the birth of Samarendra Nath Roy.

Roy was married to Bani Roy; they had four children, Prabir, Subir, Tapon and Sunandra Roy. He died while on holiday in Jasper, Canada.

**Article by:** *J J O'Connor* and *E F Robertson*

**List of References** (8 books/articles)

**Mathematicians born in the same country**

**Additional Material in MacTutor**

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