  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.
