Impact of Karl Pearson's Work on Statistical Developments in India

Nayak, Tapan K.

doi:10.1111/j.1751-5823.2009.00067.x

Cited by 6 publications

(6 citation statements)

References 33 publications

(36 reference statements)

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“…Main result. Under pH 0 q, p Z 1 n converges weakly to the multivariate normal law N p0 Gˆm , p Σq then by construction p Z n converges weakly to N p0 Gˆm , Σ 0 q where Σ 0 is defined by (22). This implies that p χ 2 n converges weakly to X 2 ppG ´1qpm 1qq as the same way as χ 2 n .…”

Section: ýñmentioning

confidence: 89%

“…Today there are many papers correcting Karl Pearson's error and which contain the proof of the goodness-of-fit chi-square test -see [11,7] for some examples of proof. Karl Pearson was a brilliant figure who influenced and developed the universe of teaching and research in statistics in the world, in particular in certain countries like India [22] and Russia [26].…”

Section: Introductionmentioning

confidence: 99%

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Exponential increase of the power of the independence and homogeneity chi-square tests with auxiliary information

Albertus

2020

Preprint

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This paper is an extension of the work about the exponential increase of the power of two non-parametric tests: the Z-test and the chi-square goodness-of-fit test. Subject to having auxiliary information, it is possible to improve exponentially relative to the size of the sample the power of the famous chi-square tests of independence and homogeneity. Improving the power of these statistical tests by using auxiliary information makes it possible either to reduce the probability of accepting the null hypothesis under the alternative hypothesis, or to reduce the size of the sample necessary to reach a predefined power. The suggested method is computational and some simple statistical applications are presented to illustrate these results. The framework of this work is non-parametric, so it can be applied to any kind of data and any area using statistics.

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Section: ýñmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Exponential increase of the power of the independence and homogeneity chi-square tests with auxiliary information

Albertus

2020

Preprint

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“…There were further publications in Biometrika by Romanovsky in 1925, 1927, 1933, and 1936, usually accompanied by an editorial comment by Karl Pearson or a paper by him. There is some further detail in Nayak (2009).There were many on Pearsonian topics, even including Pearson's name in the title, in both European and Soviet journals. The last of a series entitled “On Pearson curves” (Romanovsky, 1946) appears as the first paper in the first volume of the new publication organ of the Institute of Mathematics and Mechanics of the Uzbekistan Academy of Science.…”

Section: Romanovskymentioning

confidence: 99%

“…Pearson himself as a point of departure for the Neyman‐Pearson collaboration. Additionally, in this issue of the International Statistical Review , Nayak (2009) mentions this paper in the context of work of Mahalanobis on the “coefficients of racial likeness”, forerunners of the Mahalanobis statistic.…”

Section: Awareness Of Ra Fisher's Statistical Theorymentioning

confidence: 99%

Karl Pearson in Russian Contexts

Seneta¹

2009

Int Statistical Rev

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The confluence of statistics and probability into mathematical statistics in the Russian Empire through the interaction, 1910-1917, of A.A. Chuprov and A.A. Markov was influenced by the writings of the English Biometric School, especially those of Karl Pearson. The appearance of the Russian-language exposition of Pearsonian ideas by E. E. Slutsky in 1912 was instrumental in this confluence. Slutsky's predecessors in such writings (Lakhtin, Orzhentskii, and Leontovich) were variously of mathematical, political economy, and biological backgrounds. Work emanating from the interpolational nature of Pearson's system of frequency curves was continued subsequently through the work of Markov, Bernstein, Romanovsky, and Kravchuk (Krawtchouk), who laid a solid probabilistic foundation. The correlational nature in the interpolational early work of Chebyshev, and work of the English Biometric School in the guise of linear least-squares fitting exposited as the main component of Slutsky's book, was developed in population as well as sample context by Chuprov. He also championed the expectation operation in providing exact relations between sample and population moments, in direct interaction with Karl Pearson. Romanovsky emerges as the most adaptive and modern mathematical statistician. Copyright (c) 2009 The Author. Journal compilation (c) 2009 International Statistical Institute.

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“…In his assessment of the impact of Karl Pearson's work in the development of Statistics in India, Nayak (2009) outlined the nascent role it played in attracting Prasanta Chandra Mahalanobis to the discipline, and in inspiring him towards his eventual leading role in its development across the Indian subcontinent. See also Ghosh (1994).…”

Section: Introductionmentioning

confidence: 99%

Moments in Pearson's Four-Step Uniform Random Walk Problem and Other Applications of Very Well-Poised Generalized Hypergeometric Series

McCrorie

2020

Sankhya B

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This paper considers the representation of odd moments of the distribution of a four-step uniform random walk in even dimensions, which are based on both linear combinations of two constants representable as contiguous very well-poised generalized hypergeometric series and as even moments of the square of the complete elliptic integral of the first kind. Neither constants are currently available in closed form. New symmetries are found in the critical values of the L-series of two underlying cusp forms, providing a sense in which one of the constants has a formal counterpart. The significant roles this constant and its counterpart play in multidisciplinary contexts is described. The results unblock the problem of representing them in terms of lower-order generalized hypergeometric series, offering progress towards identifying their closed forms. The same approach facilitates a canonical characterization of the hypergeometry of the parbelos, adding to the characterizations outlined by Campbell, D'Aurozio and Sondow (2020, The American Mathematical Monthly127(1), 23-32). The paper also connects the econometric problem of characterizing the bias in the canonical autoregressive model under the unit root hypothesis to very well-poised generalized hypergeometric series. The confluence of ideas presented reflects a multidisciplinarity that accords with the approach and philosophy of Prasanta Chandra Mahalanobis.

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Impact of Karl Pearson's Work on Statistical Developments in India

Cited by 6 publications

References 33 publications

Exponential increase of the power of the independence and homogeneity chi-square tests with auxiliary information

Exponential increase of the power of the independence and homogeneity chi-square tests with auxiliary information

Karl Pearson in Russian Contexts

Moments in Pearson's Four-Step Uniform Random Walk Problem and Other Applications of Very Well-Poised Generalized Hypergeometric Series

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