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arXiv · 2106.10312

Weighted fractional generalized cumulative past entropy and its properties

Suchandan Kayal·N. Balakrishnan
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Abstract

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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Suchandan Kayal, N. Balakrishnan. 2021-06-18. Weighted fractional generalized cumulative past entropy and its properties. https://arxiv.org/abs/2106.10312

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