Inference on Curved Poisson Distribution Using Its Statistical Curvature

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Inference on Curved Poisson Distribution Using Its Statistical Curvature

Author Affiliations

¹Department of statistics, The University of Burdwan, West Bengal, INDIA
²Department of statistics, The University of Burdwan, West Bengal, INDIA

Res. J. Mathematical & Statistical Sci., Volume 1, Issue (5), Pages 6-16, June,12 (2013)

Abstract

Statistical Curvature of Bradley Efron helps in comparing curved exponential family of distributions with corresponding exponential family of distribution. The analysis in curved family has been made easy by that concept. But suitable test procedures are unavailable for discrete curved exponent families. In this paper a suitable test procedure for Curved Poisson distribution is obtained

References

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Google Scholar
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Google Scholar
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Statistical software used: R, R version 2.13.2 (2011-09-30) Copyright (C) 2011 The R Foundation for Statistical ComputingISBN 3-900051-07-0 Platform: i386-pc-mingw32/i386 (32-bit)

[ref1] Efron Bradle., Defining the Curvature of a Statistical Problem (With Applications to Second Order Efficiency)., The Annalsof Statistics, 3(6), 1189-1242, (1975)
Google Scholar

[ref2] Das Gupta A., Professor of Statistics, Purdue University, Notes on Exponential Family. (http://www.stat.purdue.edu/~dasgupta/expfamily.pdf), (year of access 2012)

[ref3] Sadhu Sanchayita, Seal Babulal, Inference in a Curved Binomial Distribution, International Journal of Statistika andMathematika, 4(2), 17-26, (2012)

[ref4] Lehmann E.L., Romano Joseph P., Testing Statistical Hypotheses, Third Edition., Springer, (2009)
Google Scholar

[ref5] Krishnamoorthy K., Handbook of Statistical Distributions with Applications, Chapman and Hall/ CRC, (2006)
Google Scholar

[ref6] Richardson Thomas and Spirtes Peter, Paremeterizing And Scoring Mixed Ancestral Graphs, Technical Report No. CMUPHIL-102,(1999)
Google Scholar

[ref7] Hunter David. R., Curved Exponential Family Models for Social Networks, Pann State University, (2006)
Google Scholar

[ref8] Lazega and Pattison (1999) and Lazega (2001), Lazega’s Lawyer Dataset,

[ref9] Ghosh R.K., Maity K.C., An Introduction to Analysis Differential Calculus Part 1, (2007)

[ref10] Apostol, Mathematical Analysis, Addison, Wesley publishing company, (1973)

[ref11] Clark David R., Thayer Charles A., A Primer on the Exponential Family of Distributions, Call Paper Program onGeneralized Linear Models, (2004)
Google Scholar

[ref12] Belloni Alexandre, Chernozhukov Vector, Posterior Inference in Curved Exponential Familiesunder Increasing Dimensions, ar Xiv: 0904.3132v2 [math.ST] (2011)
Google Scholar

[ref13] Statistical software used: R, R version 2.13.2 (2011-09-30) Copyright (C) 2011 The R Foundation for Statistical ComputingISBN 3-900051-07-0 Platform: i386-pc-mingw32/i386 (32-bit)