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Revista Colombiana de Estadística
Print version ISSN 0120-1751
Rev.Colomb.Estad. vol.44 no.2 Bogotá July/Dec. 2021 Epub Aug 30, 2021
https://doi.org/10.15446/rce.v44n2.89797
Original articles of research
Exponentiality Test Based on Progressively Type-II Censored Data Via Extension of Cumulative Tsallis Divergence
Prueba de exponencialidad basada en progresivamente tipo II Datos censurados a través de la extensión de Tsallis acumulados Divergencia
1 Department of Statistics, Ferdowsi University of Mashhad, Mashhad, Iran
In this article, first new divergences are defined by using Tsallis divergence and a measure of discrepancy between equilibriums associated with two distributions is proposed. Then utilizing the progressively Type-II censored sample, we construct goodness of fit tests for exponentiality based on the estimation of proposed divergences. To investigate the performance of the mentioned tests, Monte Carlo simulations are performed. In order to study the power, the alternatives are considered according to the failure rate function. The powers of the proposed tests are then compared with other existing tests. As regards the last step of the study, in order to explain the use of the proposed tests, three examples are presented.
Key words: Cumulative residual Tsallis divergence; Exponential distribution, Goodness of fit test; Monte Carlo simulation; Tsallis divergence
En este artículo, las primeras nuevas divergencias se definen utilizando la divergencia de Tsallis y se propone una medida de discrepancia entre los equilibrios asociados con dos distribuciones. Luego, utilizando la muestra censurada progresivamente Tipo II, construimos pruebas de bondad de ajuste para exponencialidad basadas en la estimación de divergencias propuestas. Para investigar el desempeño de las pruebas mencionadas, se realizan simulaciones Monte Carlo. Para estudiar la potencia, se consideran las alternativas según la función de tasa de falla. Los poderes de las pruebas propuestas se comparan luego con otras pruebas existentes. En cuanto al último paso del estudio, para explicar el uso de las pruebas propuestas, se presentan tres ejemplos.
Palabras clave: Bondad de ajuste; Distribución exponencial; Divergencia Tsallis; Divergencia Tsallis residual acumulada; Simulación Monte Carlo
Acknowledgement
The authors would like to thank the referees for her/his valuable comments and suggestions on an earlier version of this paper. Arezou Habibirad (corresponding author) is supported by a grant from Ferdowsi University of Mashhad (No. 2/53443).
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Received: December 2020; Accepted: March 2021
This is an open-access article distributed under the terms of the Creative Commons Attribution License
