In this paper, we introduce the cumulative past information generating function (CPIG) and relative cumulative past information generating function (RCPIG). We study its properties. We establish its relation with generalized cumulative past entropy (GCPE). We defined CPIG stochastic order and its relation with dispersive order. We provide the results for the CPIG measure of the convoluted random variables in terms of the measures of its components. We found some inequality relating to Shannon entropy, CPIG and GCPE. Some characterization and estimation results are also discussed regarding CPIG. We defined divergence measures between two random variables, Jensen-cumulative past information generating function(JCPIG), Jensen fractional cumulative past entropy measure, cumulative past Taneja entropy, and Jensen cumulative past Taneja entropy information measure.

翻译：本文引入累积过去信息生成函数（CPIG）与相对累积过去信息生成函数（RCPIG），研究其相关性质，并建立其与广义累积过去熵（GCPE）的关系。我们定义了CPIG随机序及其与分散序的关联，给出了卷积随机变量的CPIG度量与其各分量度量之间的关系式。研究表明，香农熵、CPIG与GCPE之间存在若干不等式关系。同时讨论了CPIG的若干特征化与估计方法。进一步，本文定义了两个随机变量间的散度度量，包括Jensen累积过去信息生成函数（JCPIG）、Jensen分数阶累积过去熵度量、累积过去Taneja熵及其Jensen累积过去Taneja熵信息度量。