5 research outputs found
A Shift-Dependent Measure of Extended Cumulative Entropy and Its Applications in Blind Image Quality Assessment
Recently, Tahmasebi and Eskandarzadeh introduced a new extended cumulative entropy (ECE). In this paper, we present results on shift-dependent measure of ECE and its dynamic past version. These results contain stochastic order, upper and lower bounds, the symmetry property and some relationships with other reliability functions. We also discuss some properties of conditional weighted ECE under some assumptions. Finally, we propose a nonparametric estimator of this new measure and study its practical results in blind image quality assessment
Weighted Fractional Generalized Cumulative Past Entropy
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 the
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.Comment: 23 pages, 8 figure
Weighted mean inactivity time function with applications
The concept of mean inactivity time plays a crucial role in reliability, risk
theory and life testing. In this regard, we introduce a weighted mean
inactivity time function by considering a non-negative weight function. Based
on this function, we provide expressions for the variance of transformed random
variable and the weighted generalized cumulative entropy. The latter concept is
an important measure of uncertainty which is shift-dependent and is of interest
in certain applied contexts, such as reliability or mathematical neurobiology.
Moreover, based on the comparison of mean inactivity times of a certain
function of two lifetime random variables, we introduce and study a new
stochastic order in terms of the weighted mean inactivity time function.
Several characterizations and preservation properties of the new order under
shock models, random maxima and renewal theory are discussed.Comment: 25 page
An extension of weighted generalized cumulative past measure of information
In this paper, we consider a shift-dependent measure of generalized cumulative entropy and its dynamic (past) version in the case where the weight is a general non-negative function. Our results include linear transformations, stochastic ordering, bounds and aging classes properties and some relationships with other survival concepts. We also define the conditional weighted generalized cumulative entropy and weighted generalized cumulative Kerridge inaccuracy measure. For these concepts, we obtain some properties and characterization results under suitable assumptions. Finally, we propose an estimator of this shift-dependent measure using empirical approach. In addition, we study large sample properties of this estimator