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On Cumulative Residual Renyi's Entropy
Sobre la entropía residual acumulada de Renyi
DOI:
https://doi.org/10.15446/rce.v45n2.96844Keywords:
Aging classes, Cumulative Residual Entropy, Mean residual lifetime, Stochastic Orders, Shannon Entropy, Tsallis Entropy (en)Clases de envejecimiento, Entropía residual acumulativa, Vida media residual, Órdenes estocásticas, Entropía de Shannon, Entropía Tsallis (es)
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At the entropy measures and their generalization path, in the direction of statistics and information science, recently, Sunoj & Linu (2012) proposed the cumulative residual Renyi's entropy of order α and its dynamic version and studied its main properties. In this paper, we introduce an alternative measure of cumulative residual Renyi's entropy (CRRE) of order α which, unlike the mentioned one, is positive for all distributions and all values of α. We also consider its dynamic version and study their main properties in the context of reliability theory and stochastic orders. We give an estimator of the proposed CRRE and investigate its exact and asymptotic distribution. Numerous examples illustrating the theory are also given.
En las medidas de entropía y su camino de generalización, en la dirección de las estadísticas y la ciencia de la información, recientemente, Sunoj & Linu (2012) propuso el residual acumulativo la entropía de Renyi de orden α y su versión dinámica y se estudiaron sus principales propiedades. En este artículo presentamos una medida alternativa de la entropía residual acumulada de Renyi (CRRE) de orden α que, a diferencia de la mencionada, es positiva para todas las distribuciones y todos los valores de α. También consideramos su versión dinámica y estudiamos sus principales propiedades en el contexto de la teoría de la confiabilidad y los órdenes estocásticos. Damos un estimador del CRRE propuesto e investigamos su distribución exacta y asintótica. También se dan numerosos ejemplos que ilustran la teoría.
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