Exponentiality Test Based on Progressively Type-II Censored Data Via Extension of Cumulative Tsallis Divergence

• Autores: Vahideh Ahrari, Arezou Habibirad
• Localización: Revista Colombiana de Estadística, ISSN-e 2389-8976, ISSN 0120-1751, Vol. 44, Nº. 2, 2021, págs. 297-312
• Idioma: inglés
• DOI: 10.15446/rce.v44n2.89797
• Títulos paralelos:
  • Prueba de exponencialidad basada en progresivamente tipo II Datos censurados a través de la extensión de Tsallis acumulados Divergencia
• Enlaces
  • Texto completo
• Resumen
  • español

    Resumen 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.

  • English

    Abstract 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.

• Referencias bibliográficas
  • Alizadeh Noughabi, H. (2017). 'Testing exponentiality based on kullback-leibler information for progressively type II censored data'....
  • Alizadeh Noughabi, H.,Balakrishnan, N. (2015). 'Goodness of fit using a new estimate of kullback-leibler information based on type II...
  • Balakrishnan, N. (2007). 'Progressive censoring methodology: An appraisal (with discusssions)'. Test. 16. 211
  • Balakrishnan, N.,Aggarwala, R. (2000). Progressive Censoring: Theory, Methods, and Applications. Birkhauser. Boston.
  • Balakrishnan, N.,Habibirad, A.,Arghami, N. R. (2007). 'Testing exponentiality based on kullback-leibler information with progressively...
  • Balakrishnan, N.,Lin, C.-T. (2003). 'On the distribution of a test for exponentiality based on progressively type-ii right censored spacings'....
  • Balakrishnan, N.,Sandhu, R. (1995). 'A simple simulational algorithm for generating progressive type-ii censored samples'. The American...
  • Baratpour, S.,Habibirad, A. (2016). 'Exponentiality test based on the progressive type ii censoring via cumulative entropy'. Communications...
  • Di Crescenzo, A.,Longobardi, M. (2009). 'On cumulative entropies'. Journal of Statistical Planning and Inference. 139. 4072
  • Gupta, R. C.,Kirmani, S. (1990). 'The role of weighted distributions in stochastic modeling'. Communications in Statistics-Theory...
  • Habibirad, A.,Yousefzadeh, F.,Balakrishnan, N. (2011). 'Goodness-of-ft test based on kullback-leibler information for progressively type-ii...
  • Lim, J.,Park, S. (2007). 'Censored kullback-leibler information and goodnessof-fit test with type ii censored data'. Journal of Applied...
  • Lin, C.-T.,Huang, Y.-L.,Balakrishnan, N. (2008). 'A new method for goodnessof-fit testing based on type-ii right censored samples'....
  • Nelson, W. (1982). Applied Life Data Analysis. John Wiley and Sons. New York.
  • Pakyari, R.,Balakrishnan, N. (2012). 'A general purpose approximate goodnessof-fit test for progressively type-ii censored data'....
  • Pakyari, R.,Balakrishnan, N. (2013). 'Goodness-of-fit tests for progressively type-ii censored data from location-scale distributions'....
  • Park, S.,Lim, J. (2015). 'On censored cumulative residual kullback-leibler information and goodness-of-fit test with type ii censored...
  • Park, S.,Rao, M.,Shin, D. W. (2012). 'On cumulative residual kullback-leibler information'. Statistics and Probability Letters. 82....
  • Rao, M.,Chen, Y.,Vemuri, B. C.,Wang, F.. (2004). 'Cumulative residual entropy: a new measure of information'. IEEE Transactions on...
  • Salinas, V.,Pérez, P.,González, E.,Vaquera, H. (2012). 'Goodness of fit tests for the gumbel distribution with type ii right censored...
  • Shannon, C. E. (1948). 'A mathematical theory of communication'. Bell System Technical Journal. 27. 379-423
  • Spineili, J. J.,Stephens, M. A. (1987). 'Tests for exponentiality when origin and scale parameters are unknown'. Technometrics. 29....
  • Tsallis, C. (1988). 'Possible generalization of boltzmann-gibbs statistics'. Journal of Statistical Physics. 52. 479
  • Viveros, R.,Balakrishnan, N. (1994). 'Interval estimation of parameters of life from progressively censored data'. Technometrics....
  • Wang, B. (2008). 'Goodness-of-fit test for the exponential distribution based on progressively type-II censored sample'. Journal of...
  • Yousefzadeh, F.,Arghami, N. R.. (2008). 'Testing exponentiality based on type II censored data and a new cdf estimator'. Communications...