What Is the Difference between Gamma and Gaussian Distributions?

Affiliation(s)

School of Electrical Engineering and Computer Science, University of Newcastle, Newcastle, Australia.

School of Electrical Engineering and Computer Science, University of Newcastle, Newcastle, Australia.

ABSTRACT

An inequality describing the difference between Gamma and Gaussian distributions is derived. The asymptotic bound is much better than by existing uniform bound from Berry-Esseen inequality.

KEYWORDS

Gamma Distribution; Gaussian Distribution; Berry-Esseen Inequality; Characteristic Function

Gamma Distribution; Gaussian Distribution; Berry-Esseen Inequality; Characteristic Function

Cite this paper

X. Hu, "What Is the Difference between Gamma and Gaussian Distributions?,"*Applied Mathematics*, Vol. 4 No. 2, 2013, pp. 285-289. doi: 10.4236/am.2013.42043.

X. Hu, "What Is the Difference between Gamma and Gaussian Distributions?,"

References

[1] I. S. Tyurin, “On the Accuracy of the Gaussian Approximation,” Doklady Mathematics, Vol. 80, No. 3, 2009, pp. 840-843. doi:10.1134/S1064562409060155

[2] V. Koroleva and I. Shevtsova, “An Improvement of the Berry-Essen in Equality with Application to Possion and Mixed Poison Random Sums,” Scandinavian Actuarial Journal, Vol. 2012, No. 2, 2012, pp. 81-105. doi:10.1080/03461238.2010.485370

[3] R. D. Gordon, “Values of Mills’ Ratio of Area to Bounding Ordinate and of the Normal Probability Integral for Large Values of the Argument,” The Annals of Mathematical Statistics, Vol. 12, No. 3, 1941, pp. 364-366. doi:10.1214/aoms/1177731721

[4] K. L. Chung, “A Course in Probability Theory,” 3rd Edition, Probability and Mathematical Statistics, Academic, New York, 2001.

[1] I. S. Tyurin, “On the Accuracy of the Gaussian Approximation,” Doklady Mathematics, Vol. 80, No. 3, 2009, pp. 840-843. doi:10.1134/S1064562409060155

[2] V. Koroleva and I. Shevtsova, “An Improvement of the Berry-Essen in Equality with Application to Possion and Mixed Poison Random Sums,” Scandinavian Actuarial Journal, Vol. 2012, No. 2, 2012, pp. 81-105. doi:10.1080/03461238.2010.485370

[3] R. D. Gordon, “Values of Mills’ Ratio of Area to Bounding Ordinate and of the Normal Probability Integral for Large Values of the Argument,” The Annals of Mathematical Statistics, Vol. 12, No. 3, 1941, pp. 364-366. doi:10.1214/aoms/1177731721

[4] K. L. Chung, “A Course in Probability Theory,” 3rd Edition, Probability and Mathematical Statistics, Academic, New York, 2001.