期刊
MATHEMATICS
卷 10, 期 4, 页码 -出版社
MDPI
DOI: 10.3390/math10040619
关键词
parameter estimation; gamma-exponential distribution; mixed distributions; generalized gamma distribution; generalized beta distribution; method of moments; cumulants; asymptotic normality
类别
资金
- Ministry of Science and Higher Education of the Russian Federation [075-15-2020-799]
The paper discusses the gamma-exponential distribution and the estimation of its parameters, along with the application of logarithmic cumulants method. It also addresses the difficulties associated with the inversion of polygamma functions in concentration parameter estimation.
When modeling real phenomena, special cases of the generalized gamma distribution and the generalized beta distribution of the second kind play an important role. The paper discusses the gamma-exponential distribution, which is closely related to the listed ones. The asymptotic normality of the previously obtained strongly consistent estimators for the bent, shape, and scale parameters of the gamma-exponential distribution at fixed concentration parameters is proved. Based on these results, asymptotic confidence intervals for the estimated parameters are constructed. The statements are based on the method of logarithmic cumulants obtained using the Mellin transform of the considered distribution. An algorithm for filtering out unnecessary solutions of the system of equations for logarithmic cumulants and a number of examples illustrating the results obtained using simulated samples are presented. The difficulties arising from the theoretical study of the estimates of concentration parameters associated with the inversion of polygamma functions are also discussed. The results of the paper can be used in the study of probabilistic models based on continuous distributions with unbounded non-negative support.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据