Some results on residual entropy function

Abstract

Ebrahimi and Pellerey (1995) and Ebrahimi (1996) proposed the Shannon residual entropy function as a useful dynamic measure of uncertainty. They studied the characterization problem from the residual entropy. They also used this function to define a stochastic order and two classes of distributions, DURL and IURL. In this paper, we obtain some new results on this function and we correct some mistakes in the preceding literature. Copyright Springer-Verlag 2004Life distributions, characterization, Shannon entropy, residual entropy, failure rate, stochastic orders and classes,

Interval Entropy and Informative Distance

“…The residual entropy has been used to measure the wear and tear of systems and to characterize, classify and order distributions of lifetimes. See Belzunce et al [3], Ebrahimi [4] and Ebrahimi and Kirmani [6]. Di Crescenzo and Longobardi [5] introduced the notion of past entropy and motivated its use in real-life situations.…”

“…In reliability theory and survival analysis, the residual entropy was considered in Ebrahimi and Pellerey [2], which basically measures the expected uncertainty contained in remaining lifetime of a system. The residual entropy has been used to measure the wear and tear of components and to OPEN ACCESS characterize, classify and order distributions of lifetimes by Belzunce et al [3] and Ebrahimi [4]. The notion of past entropy, which can be viewed as the entropy of the inactivity time of a system, was introduced in Di Crescenzo and Longobardi [5].…”

Stochastic Comparisons of Residual Entropy of Order Statistics and Some Characterization Results

“…In this connection, Ebrahimi (1996) proved a characterization of a lifetime distribution in terms of the residual entropy. This was followed by Belzunce et al (2004) who pointed out that the proof of Ebrahimi (1996) was not valid without some additional assumptions. Under the additional assumptions Belzunce et al (2004) proved that H(F;t) characterize the distribution.…”

“…This was followed by Belzunce et al (2004) who pointed out that the proof of Ebrahimi (1996) was not valid without some additional assumptions. Under the additional assumptions Belzunce et al (2004) proved that H(F;t) characterize the distribution. Recently Gupta (2009) presented a general result to determine whether H(F;t) or H(F;t) determine the distribution.…”

Minimum dynamic discrimination information models

“…Several authors have studied information functions that take age into account (Ebrahimi (1996), Ebrahimi and Kirmani (1996a), (1996b), Di Crescenzo and Longobardi (2002, Minimum dynamic discrimination information models 645 Belzunce et al (2004), Asadi et al (2004)). Consideration of age has led to some important insights about lifetime models, such as an information characterization of the proportional hazards model (Ebrahimi and Kirmani (1996a)) and MDE characterizations of various lifetime models, including some mixture distributions, for which no other maximum entropy formulation is available (Asadi et al (2004)).…”