In this paper, we propose R\'enyi information generating function (RIGF) and discuss its various properties. The relation between the RIGF and Shannon entropy of order $q>0$ is established. Several bounds are obtained. The RIGF of escort distribution is also derived. Furthermore, we introduce R\'enyi divergence information generating function (RDIGF) and discuss its effect under monotone transformations. Next, we propose Jensen-R\'enyi information generating function (JRIGF) and establish its properties. In addition, we present non-parametric and parametric estimators of the RIGF. For illustrative purpose, a simulation study is carried out and a real data relating to the failure times of electronic components is analyzed. Finally, a comparison study between the non-parametric and parametric estimators is made in terms of absolute bias and mean square error (MSE).

翻译：本文提出Rényi信息生成函数（RIGF）并讨论其多种性质。建立了RIGF与阶数$q>0$的香农熵之间的关系，获得了若干界。同时推导了伴随分布的RIGF。此外，本文引入Rényi散度信息生成函数（RDIGF）并讨论其在单调变换下的特性。随后提出Jensen-Rényi信息生成函数（JRIGF）并建立其性质。在估计方面，提出了RIGF的非参数与参数估计量。为说明方法，开展了模拟研究并分析了电子元件失效时间的实际数据。最后通过绝对偏差与均方误差（MSE）对非参数与参数估计量进行了比较研究。