Exponential Family Models
DOI:
https://doi.org/10.18041/1909-2458/ingeniare.12.637Keywords:
Sufficient statistic, Family exponential, sampling, Parameter, Probability functionAbstract
Many of the distributions utilized in the statistics do part of the exponential family, implying with it, a substantial advantage with regard to other models that itself do not belong to this family, advantage that is declared in significant form when is a matter of calculating the statistician of a random sample . Among the models that belong to the exponential family we have the distribution Poisson, Binomial, Normal, Gamma, Beta among others, this gives evidence of the importance of the exponential family in the modern statistical theory
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References
[1] M. Levy, “A note on nonunique MLEs and sufficient statistics”, Annals of Mathematical Statistics, vol. 39, pp. 66-80, 1985.
[2] A. Mayorga, “Inferencia Estadística. Colección Textos”, Universidad Nacional de Colombia, vol. 1, pp. 88-100, 2004.
[3] W. Navidi, “A Graphical Illustration of the EM Algorithm”, Annals of Mathematical Statistics, 51(1), pp. 30-50, 1997.
[4] O. Barndorff N., Information and Exponential Families in Statistical Theory. New York: John Wiley, 1978.
[5] E. Dynkin, Necessary and sufficient statistics for families of distributions, Uspekhi Mat. Nauk, vol. 6, pp. 68-90, 1951.
[6] H. Mann, y A. Wald, “On stochastic limit and order relationships”, annals of mathematical statistics, vol. 14, pp. 217-250, 1943.
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[8] C. Rao, “Efficient Estimates and Optimum Inference Procedures in Large Samples”, Journal of the Royal Statistical Society, vol. 24, pp. 46-55, 1962. Roberto Herrera A., Adel Mendoza M., Daniel Mendoza C. Ingeniare, Universidad Libre-Barranquilla, Año 7, No. 12, pp. 89-98 • Issn: 1909-2458 98
[9] S. Shapiro, y R. Francia, “An Approximate Analysis of Variance Test for Normality”, Journal of the American Statistical Association, vol. 67, pp. 215-230, 1972.
[10] C. Mallows, “Some comments on Cp”. Technometrics, vol. 15, pp. 661-675, 1973.
[11] D. R. Cox, and D. Hinkley, Theoretical Statistics. London: Chapman and Hall, 1974.
[12] C.R. Rao, Linear Statistical Inference and its Applications. New York: Wiley, 1965.
[2] A. Mayorga, “Inferencia Estadística. Colección Textos”, Universidad Nacional de Colombia, vol. 1, pp. 88-100, 2004.
[3] W. Navidi, “A Graphical Illustration of the EM Algorithm”, Annals of Mathematical Statistics, 51(1), pp. 30-50, 1997.
[4] O. Barndorff N., Information and Exponential Families in Statistical Theory. New York: John Wiley, 1978.
[5] E. Dynkin, Necessary and sufficient statistics for families of distributions, Uspekhi Mat. Nauk, vol. 6, pp. 68-90, 1951.
[6] H. Mann, y A. Wald, “On stochastic limit and order relationships”, annals of mathematical statistics, vol. 14, pp. 217-250, 1943.
[7] P. Bickel, y K. Doksum, Mathematical Statistics. San Francisco: Holden-Day, 1977.
[8] C. Rao, “Efficient Estimates and Optimum Inference Procedures in Large Samples”, Journal of the Royal Statistical Society, vol. 24, pp. 46-55, 1962. Roberto Herrera A., Adel Mendoza M., Daniel Mendoza C. Ingeniare, Universidad Libre-Barranquilla, Año 7, No. 12, pp. 89-98 • Issn: 1909-2458 98
[9] S. Shapiro, y R. Francia, “An Approximate Analysis of Variance Test for Normality”, Journal of the American Statistical Association, vol. 67, pp. 215-230, 1972.
[10] C. Mallows, “Some comments on Cp”. Technometrics, vol. 15, pp. 661-675, 1973.
[11] D. R. Cox, and D. Hinkley, Theoretical Statistics. London: Chapman and Hall, 1974.
[12] C.R. Rao, Linear Statistical Inference and its Applications. New York: Wiley, 1965.
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Published
2012-01-01
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How to Cite
1.
Herrera A. R, Mendoza M. A, Mendoza C D. Exponential Family Models. ingeniare [Internet]. 2012 Jan. 1 [cited 2025 Mar. 12];(12):89-98. Available from: https://revistas.unilibre.edu.co/index.php/ingeniare/article/view/637
