2021/06/18 by Suchandan Kayal, N. Balakrishnan, Kayal, Suchandan +1 · 3 citations
Mathematics · Physics and Astronomy · #Applied mathematics #Bounded function #Computer science #Cumulative distribution function #Empirical distribution function #Entropy (arrow of time) #Estimator #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical analysis #Mathematics #Measure (data warehouse) #Nonparametric statistics #Probability density function #Random variable #Statistical Distribution Estimation and Applications #Statistical Mechanics and Entropy #Statistics #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2106.10312
openalex publication_date 2021/06/18 · openalex created_date 2022/07/15 · openalex updated_date 2026/07/28
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.