In this work, we propose two information generating functions: general weighted information and relative information generating functions, and study their properties. { It is shown that the general weighted information generating function (GWIGF) is shift-dependent and can be expressed in terms of the weighted Shannon entropy. The GWIGF of a transformed random variable has been obtained in terms of the GWIGF of a known distribution. Several bounds of the GWIGF have been proposed. We have obtained sufficient conditions under which the GWIGFs of two distributions are comparable. Further, we have established a connection between the weighted varentropy and varentropy with proposed GWIGF. An upper bound for GWIGF of the sum of two independent random variables is derived. The effect of general weighted relative information generating function (GWRIGF) for two transformed random variables under strictly monotone functions has been studied. } Further, these information generating functions are studied for escort, generalized escort and mixture distributions. {Specially, we propose weighted $\beta$-cross informational energy and establish a close connection with GWIGF for escort distribution.} The residual versions of the newly proposed generating functions are considered and several similar properties have been explored. A non-parametric estimator of the residual general weighted information generating function is proposed. A simulated data set and two real data sets are considered for the purpose of illustration. { Finally, we have compared the non-parametric approach with a parametric approach in terms of the absolute bias and mean squared error values.}

翻译：本文提出了两种信息生成函数：广义加权信息生成函数与相对信息生成函数，并研究了它们的性质。研究表明，广义加权信息生成函数具有平移依赖性，且可通过加权香农熵表示。通过已知分布的广义加权信息生成函数，推导出变换后随机变量的广义加权信息生成函数表达式。提出了广义加权信息生成函数的若干界。我们获得了两种分布的广义加权信息生成函数可比较的充分条件。进一步建立了加权变熵、变熵与所提广义加权信息生成函数之间的关联。推导了两个独立随机变量之和的广义加权信息生成函数上界。研究了严格单调函数下两个变换随机变量的广义加权相对信息生成函数效应。此外，针对伴随分布、广义伴随分布及混合分布研究了这些信息生成函数的性质。特别地，我们提出了加权β-交叉信息能量，并建立了其与伴随分布的广义加权信息生成函数的紧密联系。考虑了新提出生成函数的剩余版本，并探讨了若干类似性质。提出了剩余广义加权信息生成函数的非参数估计量。通过一个模拟数据集和两个真实数据集进行例证分析。最后，在绝对偏差与均方误差值方面比较了非参数方法与参数方法的性能。