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指数型分布族熵与方差的关系
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Abstract:
熵在经济学与统计学的研究中占有重要地位。国外研究学者Mukherjee和Ratnaparkhi (1986)以图形的方式呈现了一些分布的熵和方差之间的关系。本文从指数型分布族的一般形式入手，通过熵的定义推导指数型分布族熵的一般表达形式，然后利用相关参数计算分布的方差与熵，并推导出两者之间关系的一般表达形式。
Entropy plays an important role in the research of economics and statistics. In a graphical way Mukherjee and Ratnaparkhi (1986) presented the relationship between the entropy and variance for some distributions. This paper starts from the general form of exponential distribution families, derives the general expression of entropy of exponential distribution families through the definition of entropy, and then calculates the variance and entropy of the distribution using the relevant parameters, and derives the general expression of relationship between the two.
| [1] | Holm, J. (1993) Maximum Entropy Lorenz Curves. Journal of Econometrics, 234, 20-34. |
| [2] | Maasoumi, E. (1993) A Compendium to Information Theory in Economics and Econometrics. Econometric Reviews, 12, 137-181. https://doi.org/10.1080/07474939308800260 |
| [3] | Golan, A., Judge, G.G. and Miller, D. (1996) Maximum Entropy Econometrics: Robust Estimation with Limited Data. Wiley, UK-New Jersey, 255-302. |
| [4] | Jee, D.M. and Ratnaparkhi, M.V. (1986) On the Functional Relationship between Entropy and Variance with Related Applications. Communications in Statistics-Theory and Methods, 15, 291-311. https://doi.org/10.1080/03610928608829122 |
| [5] | 杨晓珍, 李光辉. 指数型分布族的数字特征及充分统计量[J]. 凯里学院学报, 2012, 30(6): 24-26. |
| [6] | 周介南, 丁勇. 泊松分布信息熵的性质和数值计算[J]. 郑州大学学报(理学版), 2014, 46(2): 24-30. |
| [7] | 机器学习笔记之指数族分布——最大熵角度观察指数族分布(一)最大熵思想[EB/OL]. https://blog.csdn.net/qq_34758157/article/details/126247721, 2023-10-13. |
