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'''Radha Govind Laha''' (1 October 1930 – 14 July 1999) was an Indian probabilist, statistician, and mathematician, known for his work in probability theory,<ref name=LR79>{{Cite book|author=R. G. Laha and V. K. Rohatgi|year=1979|pages=557|title=Probability Theory|publisher=Wiley|location=New York.}}</ref> characteristic functions,<ref name=LL1>{{Cite book |author=E. Lukacs and R. G. Laha|title=Applications of Characteristic Functions (Griffin's Statistical Monographs & Courses, No. 14)|location=New York|publisher=T. Hafner Pub. Co.|year=1964 |pages=202}}</ref> and characterisation of distributions.<ref name=LLN60>Laha, Lukacs, and Newman (1960)</ref><ref name=Laha>Laha (1957,1958a,1958b,1959,1991,1998)</ref><ref name=LL2>Laha and Lukacs (1960,1962,1977)</ref> | '''Radha Govind Laha''' (1 October 1930 – 14 July 1999) was an Indian probabilist, statistician, and mathematician, known for his work in probability theory,<ref name=LR79>{{Cite book|author=R. G. Laha and V. K. Rohatgi|year=1979|pages=557|title=Probability Theory|publisher=Wiley|location=New York.}}</ref> characteristic functions,<ref name=LL1>{{Cite book |author=E. Lukacs and R. G. Laha|title=Applications of Characteristic Functions (Griffin's Statistical Monographs & Courses, No. 14)|location=New York|publisher=T. Hafner Pub. Co.|year=1964 |pages=202}}</ref> and characterisation of distributions.<ref name=LLN60>Laha, Lukacs, and Newman (1960)</ref><ref name=Laha>Laha (1957,1958a,1958b,1959,1991,1998)</ref><ref name=LL2>Laha and Lukacs (1960,1962,1977)</ref> | ||
==Biography== | ==Biography== | ||
===Early life=== | ===Early life=== | ||
He was born in Calcutta, India and he was a student of [[C. R. Rao]]<ref name=MathG>{{MathGenealogy|id=48987}}</ref> at [[Calcutta University]], where in 1957 he earned a doctorate in analytical probability theory from the [[Indian Statistical Institute]]. His dissertation was entitled ''Some Characterization Problems in Probability Theory and Mathematical Statistics''. | He was born in Calcutta, India and he was a student of [[C. R. Rao]]<ref name=MathG>{{MathGenealogy|id=48987}}</ref> at [[Calcutta University]], where in 1957 he earned a doctorate in analytical probability theory from the [[Indian Statistical Institute]]. His dissertation was entitled ''Some Characterization Problems in Probability Theory and Mathematical Statistics''. | ||
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Laha was the author of several classical texts on probability theory<ref name=LR79/><ref name=LL1/> and statistics<ref>{{Cite book|author=I. M. Chakrevarti, R. G. Laha and J. Roy|year=1967|title=Handbook of Methods of Applied Statistics I: Techniques of computation, descriptive methods, and statistical inference|publisher=Wiley|location=New York.}}</ref><ref>{{Cite book|author=I. M. Chakrevarti, R. G. Laha and J. Roy|year=1967|title=Handbook of Methods of Applied Statistics II: Planning of surveys and experiments|publisher=Wiley|location=New York.}}</ref> and numerous publications in journals. He was an honoured Fellow of the [[Institute of Mathematical Statistics]]<ref>{{cite web| url= http://www.imstat.org/awards/honored_fellows.htm | title = Honored IMS Fellows | access-date = 1 March 2011}}</ref> and an elected member of the [[International Statistical Institute]]. | Laha was the author of several classical texts on probability theory<ref name=LR79/><ref name=LL1/> and statistics<ref>{{Cite book|author=I. M. Chakrevarti, R. G. Laha and J. Roy|year=1967|title=Handbook of Methods of Applied Statistics I: Techniques of computation, descriptive methods, and statistical inference|publisher=Wiley|location=New York.}}</ref><ref>{{Cite book|author=I. M. Chakrevarti, R. G. Laha and J. Roy|year=1967|title=Handbook of Methods of Applied Statistics II: Planning of surveys and experiments|publisher=Wiley|location=New York.}}</ref> and numerous publications in journals. He was an honoured Fellow of the [[Institute of Mathematical Statistics]]<ref>{{cite web| url= http://www.imstat.org/awards/honored_fellows.htm | title = Honored IMS Fellows | access-date = 1 March 2011}}</ref> and an elected member of the [[International Statistical Institute]]. | ||
Laha was particularly interested in characterisations of the normal distribution.<ref name=Laha-bio2 /><ref>Radha G. Laha (obituary), The Toledo Blade, 18 July 1999.</ref> One of his well-known results is his disproof of a long-standing conjecture: that the ratio of two independent, identically distributed random variables is Cauchy distributed if and only if the variables have normal distributions. Laha became known for disproving this conjecture.<ref>{{cite journal|journal = Proceedings of the National Academy of Sciences | author = R. G. Laha | year = 1958 | volume = 44 | pages = 222–223 | title = An Example of a Nonnormal Distribution where the Quotient Follows the Cauchy Law| url = http://www.pnas.org/content/44/2/222.full.pdf | issue=2|doi = 10.1073/pnas.44.2.222| pmc = 335393 | pmid=16590171}}</ref> Laha also proved several generalisations of the classical characterisation of normal sample distribution by the independence of sample mean and sample variance.<ref>Laha (1991)</ref> | Laha was particularly interested in characterisations of the normal distribution.<ref name=Laha-bio2 /><ref>Radha G. Laha (obituary), The Toledo Blade, 18 July 1999.</ref> One of his well-known results is his disproof of a long-standing conjecture: that the ratio of two independent, identically distributed random variables is Cauchy distributed if and only if the variables have normal distributions. Laha became known for disproving this conjecture.<ref>{{cite journal|journal = Proceedings of the National Academy of Sciences | author = R. G. Laha | year = 1958 | volume = 44 | pages = 222–223 | title = An Example of a Nonnormal Distribution where the Quotient Follows the Cauchy Law| url = http://www.pnas.org/content/44/2/222.full.pdf | issue=2|doi = 10.1073/pnas.44.2.222| pmc = 335393 | pmid=16590171| bibcode = 1958PNAS...44..222L | doi-access = free }}</ref> Laha also proved several generalisations of the classical characterisation of normal sample distribution by the independence of sample mean and sample variance.<ref>Laha (1991)</ref> | ||
===Philanthropist=== | ===Philanthropist=== | ||
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* Laha, R. G. (1991). A characterisation of Gaussian law in Hilbert space, ''[[Aequationes Mathematicae]]'' 41 (1991), no. 1, 85–93. | * Laha, R. G. (1991). A characterisation of Gaussian law in Hilbert space, ''[[Aequationes Mathematicae]]'' 41 (1991), no. 1, 85–93. | ||
* {{cite journal | last1 = Laha | first1 = R. G. | last2 = Lukacs | first2 = E. | year = 1977 | title = On a functional equation which occurs in a characterization problem | journal = [[Aequationes Mathematicae]] | volume = 16 | issue = 3| pages = 259–274 | doi = 10.1007/BF01836038 | s2cid = 122866588 }} | * {{cite journal | last1 = Laha | first1 = R. G. | last2 = Lukacs | first2 = E. | year = 1977 | title = On a functional equation which occurs in a characterization problem | journal = [[Aequationes Mathematicae]] | volume = 16 | issue = 3| pages = 259–274 | doi = 10.1007/BF01836038 | s2cid = 122866588 }} | ||
* {{cite journal | last1 = Laha | first1 = R. G. | year = 1964 | title = On the decomposition of a class of functions of bounded variation | journal = Can. J. Math. | volume = 16 | pages = 479–484 | doi = 10.4153/CJM-1964-049-8 }} | * {{cite journal | last1 = Laha | first1 = R. G. | year = 1964 | title = On the decomposition of a class of functions of bounded variation | journal = Can. J. Math. | volume = 16 | pages = 479–484 | doi = 10.4153/CJM-1964-049-8 | s2cid = 124766763 }} | ||
* {{cite journal | last1 = Laha | first1 = R. G. | last2 = Lukacs | first2 = E. | year = 1962 | title = On a factorization of characteristic functions which have a finite number of derivatives at the origin | journal = Publ. Inst. Statist. Univ. Paris | volume = 11 | pages = 221–224 }} | * {{cite journal | last1 = Laha | first1 = R. G. | last2 = Lukacs | first2 = E. | year = 1962 | title = On a factorization of characteristic functions which have a finite number of derivatives at the origin | journal = Publ. Inst. Statist. Univ. Paris | volume = 11 | pages = 221–224 }} | ||
* {{cite journal | last1 = Laha | first1 = R. G. | last2 = Lukacs | first2 = E. | year = 1964 | title = On a problem connected with quadratic regression | journal = Biometrika | volume = 47 | issue = 3–4| pages = 335–343 | doi=10.1093/biomet/47.3-4.335}} | * {{cite journal | last1 = Laha | first1 = R. G. | last2 = Lukacs | first2 = E. | year = 1964 | title = On a problem connected with quadratic regression | journal = Biometrika | volume = 47 | issue = 3–4| pages = 335–343 | doi=10.1093/biomet/47.3-4.335}} | ||
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* {{cite journal | last1 = Laha | first1 = R. G. | year = 1959 | title = On the laws of Cauchy and Gauss | journal = Annals of Mathematical Statistics | volume = 30 | issue = 4| pages = 1165–1174 | doi = 10.1214/aoms/1177706102 | doi-access = free }} | * {{cite journal | last1 = Laha | first1 = R. G. | year = 1959 | title = On the laws of Cauchy and Gauss | journal = Annals of Mathematical Statistics | volume = 30 | issue = 4| pages = 1165–1174 | doi = 10.1214/aoms/1177706102 | doi-access = free }} | ||
* {{cite journal | last1 = Laha | first1 = R. G. | year = 1958a | title = On a factorization theorem in the theory of analytic characteristic functions | journal = Annals of Mathematical Statistics | volume = 29 | issue = 3| pages = 922–926 | doi = 10.1214/aoms/1177706553 | doi-access = free }} | * {{cite journal | last1 = Laha | first1 = R. G. | year = 1958a | title = On a factorization theorem in the theory of analytic characteristic functions | journal = Annals of Mathematical Statistics | volume = 29 | issue = 3| pages = 922–926 | doi = 10.1214/aoms/1177706553 | doi-access = free }} | ||
* {{cite journal | last1 = Laha | first1 = R. G. | year = 1958b | title = An example of a nonnormal distribution where the quotient follows the Cauchy law | journal = Proc. Natl. Acad. Sci. USA | volume = 44 | issue = 2| pages = 222–223 | doi = 10.1073/pnas.44.2.222 | pmc = 335393 | pmid=16590171}} | * {{cite journal | last1 = Laha | first1 = R. G. | year = 1958b | title = An example of a nonnormal distribution where the quotient follows the Cauchy law | journal = Proc. Natl. Acad. Sci. USA | volume = 44 | issue = 2| pages = 222–223 | doi = 10.1073/pnas.44.2.222 | pmc = 335393 | pmid=16590171| bibcode = 1958PNAS...44..222L | doi-access = free }} | ||
* {{cite journal | last1 = Roy | first1 = J. | last2 = Laha | first2 = R. G. | year = 1957 | title = On partially balanced linked block designs | journal = Annals of Mathematical Statistics | volume = 28 | issue = 2| pages = 488–493 | doi = 10.1214/aoms/1177706977 | doi-access = free }} | * {{cite journal | last1 = Roy | first1 = J. | last2 = Laha | first2 = R. G. | year = 1957 | title = On partially balanced linked block designs | journal = Annals of Mathematical Statistics | volume = 28 | issue = 2| pages = 488–493 | doi = 10.1214/aoms/1177706977 | doi-access = free }} | ||
* {{cite journal | last1 = Laha | first1 = R. G. | year = 1957 | title = On some characterization problems connected with linear structural relations | journal = Annals of Mathematical Statistics | volume = 28 | issue = 2| pages = 405–414 | doi = 10.1214/aoms/1177706968 | doi-access = free }} | * {{cite journal | last1 = Laha | first1 = R. G. | year = 1957 | title = On some characterization problems connected with linear structural relations | journal = Annals of Mathematical Statistics | volume = 28 | issue = 2| pages = 405–414 | doi = 10.1214/aoms/1177706968 | doi-access = free }} | ||