Further results on the generalized cumulative entropy

Antonio Di Crescenzo; Abdolsaeed Toomaj

Kybernetika (2017)

  • Volume: 53, Issue: 5, page 959-982
  • ISSN: 0023-5954

Abstract

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Recently, a new concept of entropy called generalized cumulative entropy of order n was introduced and studied in the literature. It is related to the lower record values of a sequence of independent and identically distributed random variables and with the concept of reversed relevation transform. In this paper, we provide some further results for the generalized cumulative entropy such as stochastic orders, bounds and characterization results. Moreover, some characterization results are derived for the dynamic generalized cumulative entropy. Finally, it is shown that the empirical generalized cumulative entropy of an exponential distribution converges to normal distribution.

How to cite

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Di Crescenzo, Antonio, and Toomaj, Abdolsaeed. "Further results on the generalized cumulative entropy." Kybernetika 53.5 (2017): 959-982. <http://eudml.org/doc/294423>.

@article{DiCrescenzo2017,
abstract = {Recently, a new concept of entropy called generalized cumulative entropy of order $n$ was introduced and studied in the literature. It is related to the lower record values of a sequence of independent and identically distributed random variables and with the concept of reversed relevation transform. In this paper, we provide some further results for the generalized cumulative entropy such as stochastic orders, bounds and characterization results. Moreover, some characterization results are derived for the dynamic generalized cumulative entropy. Finally, it is shown that the empirical generalized cumulative entropy of an exponential distribution converges to normal distribution.},
author = {Di Crescenzo, Antonio, Toomaj, Abdolsaeed},
journal = {Kybernetika},
keywords = {generalized cumulative entropy; lower record values; reversed relevation transform; stochastic orders; parallel system},
language = {eng},
number = {5},
pages = {959-982},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Further results on the generalized cumulative entropy},
url = {http://eudml.org/doc/294423},
volume = {53},
year = {2017},
}

TY - JOUR
AU - Di Crescenzo, Antonio
AU - Toomaj, Abdolsaeed
TI - Further results on the generalized cumulative entropy
JO - Kybernetika
PY - 2017
PB - Institute of Information Theory and Automation AS CR
VL - 53
IS - 5
SP - 959
EP - 982
AB - Recently, a new concept of entropy called generalized cumulative entropy of order $n$ was introduced and studied in the literature. It is related to the lower record values of a sequence of independent and identically distributed random variables and with the concept of reversed relevation transform. In this paper, we provide some further results for the generalized cumulative entropy such as stochastic orders, bounds and characterization results. Moreover, some characterization results are derived for the dynamic generalized cumulative entropy. Finally, it is shown that the empirical generalized cumulative entropy of an exponential distribution converges to normal distribution.
LA - eng
KW - generalized cumulative entropy; lower record values; reversed relevation transform; stochastic orders; parallel system
UR - http://eudml.org/doc/294423
ER -

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