{"title":"Quantile-based information generating functions and their properties and uses","authors":"Suchandan Kayal, N. Balakrishnan","doi":"10.1017/s0269964824000068","DOIUrl":null,"url":null,"abstract":"\n Information generating functions (IGFs) have been of great interest to researchers due to their ability to generate various information measures. The IGF of an absolutely continuous random variable (see Golomb, S. (1966). The information generating function of a probability distribution. IEEE Transactions in Information Theory, 12(1), 75–77) depends on its density function. But, there are several models with intractable cumulative distribution functions, but do have explicit quantile functions. For this reason, in this work, we propose quantile version of the IGF, and then explore some of its properties. Effect of increasing transformations on it is then studied. Bounds are also obtained. The proposed generating function is studied especially for escort and generalized escort distributions. Some connections between the quantile-based IGF (Q-IGF) order and well-known stochastic orders are established. Finally, the proposed Q-IGF is extended for residual and past lifetimes as well. Several examples are presented through out to illustrate the theoretical results established here. An inferential application of the proposed methodology is also discussed","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Probability in the Engineering and Informational Sciences","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1017/s0269964824000068","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ENGINEERING, INDUSTRIAL","Score":null,"Total":0}
引用次数: 0
Abstract
Information generating functions (IGFs) have been of great interest to researchers due to their ability to generate various information measures. The IGF of an absolutely continuous random variable (see Golomb, S. (1966). The information generating function of a probability distribution. IEEE Transactions in Information Theory, 12(1), 75–77) depends on its density function. But, there are several models with intractable cumulative distribution functions, but do have explicit quantile functions. For this reason, in this work, we propose quantile version of the IGF, and then explore some of its properties. Effect of increasing transformations on it is then studied. Bounds are also obtained. The proposed generating function is studied especially for escort and generalized escort distributions. Some connections between the quantile-based IGF (Q-IGF) order and well-known stochastic orders are established. Finally, the proposed Q-IGF is extended for residual and past lifetimes as well. Several examples are presented through out to illustrate the theoretical results established here. An inferential application of the proposed methodology is also discussed
信息生成函数(IGF)因其生成各种信息量的能力而备受研究人员关注。绝对连续随机变量的 IGF(见 Golomb, S. (1966)。概率分布的信息生成函数。IEEE Transactions in Information Theory, 12(1), 75-77)取决于其密度函数。但是,有几个模型的累积分布函数难以实现,但却有明确的量子函数。因此,在本研究中,我们提出了量子版本的 IGF,并探讨了它的一些特性。然后研究了增量变换对它的影响。此外,我们还获得了边界。我们特别针对护送分布和广义护送分布研究了所提出的生成函数。建立了基于量子的 IGF(Q-IGF)阶次与著名随机阶次之间的一些联系。最后,提出的 Q-IGF 还扩展到了残差和过去寿命。为了说明本文所建立的理论结果,本文列举了几个实例。还讨论了所提方法的推理应用
期刊介绍:
The primary focus of the journal is on stochastic modelling in the physical and engineering sciences, with particular emphasis on queueing theory, reliability theory, inventory theory, simulation, mathematical finance and probabilistic networks and graphs. Papers on analytic properties and related disciplines are also considered, as well as more general papers on applied and computational probability, if appropriate. Readers include academics working in statistics, operations research, computer science, engineering, management science and physical sciences as well as industrial practitioners engaged in telecommunications, computer science, financial engineering, operations research and management science.