论文标题
在广义Gini和Gini的限制下，Mathai的熵最大化，均值差异指数及其在保险中的应用
Maximization of Mathai's Entropy under the Constraints of Generalized Gini and Gini mean difference indices and its Applications in Insurance
论文作者
论文摘要
统计物理学，扩散熵分析和信息理论通常使用Mathai的熵，该熵衡量了概率定律的随机性，而福利经济学和社会科学通常使用衡量概率法律均匀性的Gini指数。在最大熵的原理中，我们探索了Mathai的熵的最大化，但在以下情况下，根据条件：（i）密度函数和固定均值的条件； （ii）密度函数和固定广义Gini指数的条件。我们还可以根据给定的Gini平均差异指数的约束和密度函数的条件最大化Mathai的熵。从1971年到1994年，获得的最大熵分布适用于加利福尼亚地震保险的损失比（年度数据），并比较了其具有一些单参数分布的性能。
Statistical Physics, Diffusion Entropy Analysis and Information Theory commonly use Mathai's entropy which measures the randomness of probability laws, whereas welfare economics and the Social Sciences commonly use Gini index which measures the evenness of probability laws. Motivated by the principle of maximal entropy, we explore the maximization of Mathai's entropy subject to the conditions in the following scenarios: (i) the conditions of a density function and fixed mean; (ii) the conditions of a density function and fixed Generalized Gini index. We also maximizes the Mathai's entropy subject to the constraints of a given Gini mean difference index and the conditions of a density function. The obtained maximum entropy distribution is fitted to the loss ratios (yearly data) for earthquake insurance in California from 1971 through 1994 and its performance with some one-parameter distributions are compared.
