جستجوی مقالات مرتبط با کلیدواژه « past entropy » در نشریات گروه « آمار »

The main measure of the uncertainty contained in random variable X is the Shannon entropy H(X) = −E(log(f(X)). The cumulative entropy is an information measure which is alternative to the Shannon entropy and is connected with reliability theory. The cumulative residual entropy (CRE) introduced by Rao et al. (2004) is a generalized measure of uncertainty which is applied in reliability. Asadi and Zohrevand (2007) defined a dynamic version of the CRE by ε(X,t). In this paper, weighted residual entropy and weighted cumulative residual entropy are discussed. The properties of weighted entropy, cumulative residual entropy, weighted residual entropy, weighted cumulative residual entropy, weighted past entropy, weighted cumulative past entropy, dynamic cumulative residual entropy, dynamic cumulative past entropy, are also given.

Di Crescenzo and Longobardi (2002) has been proposed a measure of uncertainty related to past life namely past entropy. The present paper addresses the question of extending this concept to bivariate set-up and study some properties of the proposed measure. It is shown that the proposed measure uniquely determines the distribution function. Characterizations for some bivariate lifetime models are obtained using the proposed measure. Further, we define new classes of life distributions based on this measure and properties of the new classes are also discussed. We also proposed a non-parametric kernel estimator for the proposed measure and illustrated performance of the estimator using a numerical data.