加权分数广义累积过去熵及其性质
Weighted fractional generalized cumulative past entropy and its properties
摘要：
本文引入了非负绝对连续随机变量在有界支撑下的加权分式广义累积过去熵。各种性质的建议加权分数测度进行了研究。边界和随机排序。建立了该测度与左Riemann-Liouville分数次积分之间的联系。进一步，研究了比例反向风险率模型的测度。其次，基于经验分布函数，提出了加权分数广义累积过去熵的非参数估计。出于说明的目的，考虑了具有真实生活数据集的各种示例。最后，研究了所提出的经验估计量的大样本性质。
英文摘要：
In this paper, we introduce weighted fractional generalized cumulative past entropy of a nonnegative absolutely continuous random variable with bounded support. Various properties of the proposed weighted fractional measure are studied. Bounds and stochastic orderings are derived. A connection between the proposed measure and the left-sided Riemann-Liouville fractional integral is established. Further, the proposed measure is studied for the proportional reversed hazard rate models. Next, a nonparametric estimator of the weighted fractional generalized cumulative past entropy is suggested based on empirical distribution function. Various examples with a real life data set are considered for the illustration purposes. Finally, large sample properties of the proposed empirical estimator are studied.
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