>Ghosh sarbajit at 12:26, 9 October 2021

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{{short description|Indian statistician}}
{{Use Indian English|date=May 2015}}
{{Use dmy dates|date=May 2015}}
{{Infobox scientist
|name = Anil Kumar Bhattacharya
|image =
|caption =
|birth_date = {{Birth date|1915|04|01|df=yes}}
|birth_place = Bhatpara, [[Bengal Presidency]], [[British India]] (Now [[West Bengal]], [[India]])
|residence =
|citizenship = [[India]]
|death_date = {{Death date and age|1996|07|17|1915|04|01|df=yes}}
|death_place =
|field = [[Statistician]]
|work_institution = [[University of Calcutta]], [[Indian Statistical Institute]]
|alma_mater = [[Rajabazar Science College]]<br>([[University of Calcutta]])
|doctoral_students =
|known_for = [[Bhattacharyya distance]], Bhattacharyya bound
|prizes =
|footnotes =
}}

'''Anil Kumar Bhattacharya''' ({{lang-bn|অনিল কুমার ভট্টাচার্য}}; also spelled '''Anil Kumar Bhattacharyya''') (1 April 1915 – 17 July 1996) was an Indian [[statistician]] who worked at the [[Indian Statistical Institute]] in the 1930s and early 40s. He made fundamental contributions to [[multivariate statistics]], particularly for his measure of similarity between two multinomial distributions, known as the [[Bhattacharya coefficient]], based on which he defined a [[Metric (mathematics)|metric]], the [[Bhattacharya distance]]. This measure is widely used in comparing statistical samples in biology, physics, computer science, etc.

Distance between statistical distributions had been addressed in 1936 by Mahalanobis, who proposed the D<sup>2</sup> metric, now known as [[Mahalanobis distance]]. Subsequently, Bhattacharya defined a [[cosine similarity|cosine metric]] for distance between distributions, in a [[Calcutta Mathematical Society]] paper in 1943,<ref>{{cite journal
|first=A. |last=Bhattacharyya
|title=On a measure of divergence between two statistical populations defined by their probability distributions
|journal=[[Calcutta Mathematical Society]]
|volume=35 |pages=99–109 |year=1943
|mr=0010358
}}
</ref><ref name=":0" /> expanding on some of the results in another paper in [[Sankhya (journal)|Sankhya]] in 1947. Bhattacharyya's two major research concerns were the measurement of divergence between two probability distributions and the setting of lower bounds to the variance of an unbiased estimator.

==Life==
Bhattacharya was born to Bhavanath and Lilavati, sometime in March–April 1915 (in the month Chaitra [[Bengali language|Bengali]]: চৈত্র of the year 1321, the exact date is not known)<ref name=Festschrift>{{cite book
| title = Essays on probability and statistics: Festschrift in honour of Professor Anil Kumar Bhattacharya
|author1=S. P. Mukherjee |author2=Arijit Chaudhuri |author3=Sujit K. Basu | editor = A. M. Gun on behalf of the Organizing Committee, Golden Jubilee Celebrations
| publisher = Department of Statistics, Presidency College
| year = 1994 }}</ref> at [[Bhatpara]] in the district of [[24 Parganas]] of [[West Bengal]]. He passed the [[Matriculation Examination]] of [[Calcutta University]] in 1932 and [[Indian School Certificate|I. Sc. Examination]] in 1934 from Hooghly Mohshin College. In 1936 he ranked first in the First Class at the B.A./B.Sc. examination from the same college and went over to the renowned [[Rajabazar Science College|Science College]], [[Calcutta University]] for an M.Sc. in Mathematics. Here he had F. W. Levy and [[Raj Chandra Bose]] as his teachers and passed the M.A. Examination in 1938 with the first rank in the First Class.

In 1939, at Levy's suggestion, Bhattacharya met [[Prasanta Chandra Mahalanobis|P. C. Mahalanobis]] and joined [[Indian Statistical Institute]] as an honorary worker.<ref name=crrao>[[C R Rao]], Prasantha Chandra Mahalanobis (1893-1972), [[Biographical Memoirs of Fellows of the Royal Society]], v.19 (Dec 1973), pp.455-492</ref> In 1941, he was made a part-time lecturer in the newly formed Statistics Department of [[Calcutta University]], headed by [[Mahalanobis]]. Here he had [[C. R. Rao]], H. K. Nandi and T. P. Choudhury, as his students. He went to [[Patna]] to take up the job of Statistical Officer of [[Bihar]] Government, in December 1943 and, in 1946, he returned to [[Calcutta]] to join [[Indian Statistical Institute]] as Superintending Statistician (in charge of training). Mahalanobis requested him to concurrently take classes in the Statistics Department of [[Presidency University, Kolkata|Presidency College]]. After the post was created, Bhattacharya was made a whole-time Senior Professor and Head of the Department in 1949. He occupied the post of Senior Professor until his retirement in March 1974, but in 1967 he stepped down from the leadership, apparently piqued by certain moves of the [[West Bengal]] Government's Education Department.<ref name="Festschrift"/> Almost since his retirement from Government service, he had been associated with the Narendrapur [[Ramakrishna Mission Residential College]] as a guest teacher, where a Memorial Scholarship is awarded in his name.<ref>{{cite web|url=http://www.rkmcnarendrapur.org/index1.php?page=scholarship/ |title=www.rkmcnarendrapur.org/index1.php?page=scholarship/ |publisher=Rkmcnarendrapur.org |access-date=2013-02-25}}</ref>

==Works==
"A note on Ramamurti's problem of maximal sets", ''Sankhya'', 6 (1942) 189 - 192. <ref>{{cite journal |last1=Bhattacharyya |first1=A. |title=A Note on Ramamurti's Problem of Maximal Sets |journal=Sankhyā |url=https://www.jstor.org/stable/25047757}}</ref>

"On a measure of divergence between two statistical populations defined by their probability distributions", ''Bull. Cal. Math. Soc'', 35 (1943) 99 - 109. <ref name=":0">{{cite journal |author1-link=On a measure of divergence between two statistical populations defined by their probability distributions. |title=Bulletin of the Calcutta Mathematical Society, Vol-35 |date=1943 |url=https://www.caluniv.ac.in/digital-lib-dev/ebook/pdf_view.php?pdflink=https://s3.ap-south-1.amazonaws.com/calcutta-university/departmental-journals/H00603.pdf&cat_type=A |quote=Article: "On a measure of divergence between two statistical populations defined by their probability distributions" is in Page: 99-109}}</ref>

"On some sets of sufficient conditions leading to the normal bivariate distribution", ''Sankhya'', 6 (1943) 399 - 406. <ref>{{cite journal |last1=Bhattacharyya |first1=A. |title=On Some Sets of Sufficient Conditions Leading to the Normal Bivariate Distribution |journal=Sankhyā |url=https://www.jstor.org/stable/25047806}}</ref>

"A note on the distribution of the sum of chi-squares", ''Sankhya'', 7 (1945), 27 - 28. <ref>{{cite journal |last1=Bhattacharyya |first1=A. |title=A Note on the Distribution of the Sum of Chi-Squares |journal=Sankhyā |url=https://www.jstor.org/stable/25047828}}</ref>

"On some analogues of the amount of information and their uses in statistical estimation" I, ''Sankhya'', 8 (1946) 1 - 14. <ref>{{cite journal |last1=Bhattacharyya |first1=A. |title=On Some Analogues of the Amount of Information and Their Use in Statistical Estimation |journal=Sankhyā |url=https://www.jstor.org/stable/25047921}}</ref>

"On some analogues of the amount of information and their uses in statistical estimation" II, ''Sankhya'', 8 (1947) 201 - 218. <ref>{{cite journal |last1=Bhattacharyya |first1=A. |title=On Some Analogues of the Amount of Information and Their Use in Statistical Estimation (Contd.) |journal=Sankhyā |url=https://www.jstor.org/stable/25047948}}</ref>

"On some analogues of the amount of information and their uses in statistical estimation" III, ''Sankhya'', 8 (1948) 315 - 328. <ref>{{cite journal |last1=Bhattacharyya |first1=A. |title=On Some Analogues of the Amount of Information and Their Use in Statistical Estimation (Concluded) |journal=Sankhyā |url=https://www.jstor.org/stable/25047897}}</ref>

"On a measure of divergence between two multinomial populations", ''Sankhya'', 7 (1946), 401 - 406. <ref>{{cite journal |last1=Bhattacharyya |first1=A. |title=On a Measure of Divergence between Two Multinomial Populations |journal=Sankhyā |url=https://www.jstor.org/stable/25047882}}</ref>

"Unbiased statistics with minimum variance", ''Proc. Roy. Soc. Edin.'', A, 63 (1950), 69 - 77.

"The theory of regression in statistical population admitting local parameters", ''Bull. Int. Stat. Inst.'', 33, Part II (1951).

"On some uses of the t-distribution in multivariate analysis", ''Sankhya'', 12 (1952), 89 - 104. <ref>{{cite journal |last1=Bhattacharyya |first1=A. |title=On the Uses of the t-Distribution in Multivariate Analysis |journal=Sankhyā |url=https://www.jstor.org/stable/25048117}}</ref>

"Notes on the use of unbiased and biased statistics in the binomial population", ''Cal. Stat. Assoc. Bull''., 5 (1954), 149 - 164.

"Some uses of the 'amount of information' in the statistical inference", (address of the Sectional President), ''Proc. Ind. Sc. Cong''., 46th Session (1959).

"On a geometrical representation of probability distribution and its use in statistical inference", ''Cal. Stat. Assoc. Bull.'', 40 (1990–91), 23 - 49. <ref>{{cite journal |last1=Bhattacharyya |first1=A. |title=On a Geometrical Representation of Probability Distributions and its use in Statistical Inference |journal=Calcutta Statistical Association Bulletin |doi=10.1177/0008068319900504 |url=https://doi.org/10.1177%2F0008068319900504}}</ref>

==References==
<references/>

==External links==
*[https://web.archive.org/web/20170124233611/http://sankhya.isical.ac.in/search/57a1/57a1017.pdf Essays on probability and statistics: Festschrift in honour of Professor Anil Kumar Bhattacharyya]

*[https://doi.org/10.1177%2F0008068319960301 Anil Kumar Bhattacharyya (1915-1996): A Reverent Remembrance] by [[Pranab K. Sen]]

{{Indian mathematics}}

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{{DEFAULTSORT:Bhattacharya, Anil}}
[[Category:Bengali scientists]]
[[Category:Indian Statistical Institute faculty]]
[[Category:Indian statisticians]]
[[Category:1915 births]]
[[Category:1996 deaths]]
[[Category:People from Bhatpara]]
[[Category:University of Calcutta alumni]]
[[Category:University of Calcutta faculty]]
[[Category:20th-century Indian mathematicians]]
[[Category:Scientists from West Bengal]]
[[Category:Anil Kumar Bhattacharya]]

Anil Kumar Bhattacharya - Revision history

>Ghosh sarbajit at 12:26, 9 October 2021