【摘要】 基于最大Rényi熵原理,在归一化和均值约束下,提出了一种具有封闭表达式的双参数广义指数分布,记为q-指数分布。该文研究了该分布的统计性质,指出可以分别利用极大似然法和信息似然法估计q-指数分布参数,并将该分布用于可靠性分析。利用两个已知的数据集进行了验证,实验结果表明,所提出的q-指数分布比其他常用分布,如韦伯分布和线性失效率分布,能够更好地拟合数据集。此外,锂电池剩余寿命估计实验表明,采用q-指数分布比采用传统指数分布,估计精度至少提高17.857%。更多还原

【Abstract】 We propose a two-parameter generalized exponential distribution with closed-form expression based on the maximum Rényi entropy principle under the normalization and mean constraints, which is referred as the q-exponential distribution. The statistical properties of this distribution are investigated. The maximum likelihood method and information likelihood method are used to estimate the parameters of the proposed distribution, respectively. Two well-known data sets are employed to evaluate the q-exponential distribution, and the experimental results demonstrate that the proposed distribution can fit the data sets better than other wellknown distributions, such as Weibull distribution and linear failure rate distribution. Additionally, the experiment results of life estimation of the Li-ion batteries prove that compared with the exponential distribution, the proposed distribution can give more accurate prediction. In the last experiment, the estimation accuracy is improved by at least 17.857%.更多还原