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：本文介绍了累积过去信息生成函数（CPIG）和相对累积过去信息生成函数（RCPIG）。我们研究了其性质，建立了其与广义累积过去熵（GCPE）的关系，定义了CPIG随机序及其与分散序的联系。针对卷积随机变量的CPIG度量，我们给出了基于其分量度量的结果，并发现了一些与香农熵、CPIG和GCPE相关的不等式。此外，还讨论了CPIG的刻画与估计结果。我们定义了两个随机变量之间的散度度量，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熵以及Jensen累积过去Taneja熵信息度量。