¹University of Isfahan, Department of Statistics, Isfahan, Iran. PhD. Email: e.zamanzade@sci.ui.ac.ir; ehsanzamanzadeh@yahoo.com
²Hakim Sabzevari University, Department of Statistics, Sabzevar, Iran. PhD. Email: mahdizadeh.m@live.com

In this paper, we develop some goodness of fit tests for Rayleigh distribution based on Phi-divergence. Using Monte Carlo simulation, we compare the power of the proposed tests with some traditional goodness of fit tests including Kolmogorov-Smirnov, Anderson-Darling and Cramer von-Mises tests. The results indicate that the proposed tests perform well as compared with their competing tests in the literature. Finally, the new procedures are illustrated via two real data sets.

Key words: Goodness of fit test, Monte Carlo simulation, Phi-divegence, Rayleigh distribution.

En este artículo desarrollamos pruebas de bondadn de ajuste para distribución Rayleigh basados en divergencia Phi. Usando simulaciones de Monte Carlo, comparamos el poder de las pruebas propuestas con algunas pruebas tradicionales incluyendo Kolmogorov-Smirnov, Anderson-Darling y Cramer von-Mises. Los resultados indican que la prueba propuesta funciona mejor que las otras pruebas reportadas en literatura. Finalmente, los procedimientos nuevos son ilustrados sobre dos conjuntos de datos reales.

Palabras clave: distribución Rayleigh, Divergencia Phi, Pruebas de bondad de ajuste, Simulaciones Monte Carlo.

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References

1. Alizadeh Noughabi, H. & Balakrishnan, N. (2016), 'Tests of goodness of fit based on Phi-divergence', Journal of Applied Statistics 43(3), 412-429.         [ Links ]

2. Alizadeh Noughabi, R., Alizadeh Noughabi, H. & Ebrahimi Moghaddam Behdadi, A. (2014), 'An entropy test for the rayleigh distribution and power comparison', Journal of Statistical Computation and Simulation 84(1), 151-158.         [ Links ]

3. Best, D., Rayner, J. & Thas, O. (2010), 'Easily applied tests of fit for the Rayleigh distribution', Synkhya, B 72, 254-263.         [ Links ]

4. Csiszar, I. (1967), 'On topology properties of f-divergences', Studia Scientiarum Mathematicarum Hungarica 2, 329-339.         [ Links ]

5. Dey, S., Dey, T. & Kundu, D. (2014), 'Two parameter Rayleigh distribution: Different methods of estimation', merican Journal of Mathematical and Management Sciences 33(1), 55-74.         [ Links ]

6. Jahanshahi, S., Habibi Rad, A. & Fakoor, V. (2016), 'A goodness-of-fit test for Rayleigh distribution based on Helinger distance', Annals of Data Sciences 3(4), 401-411.         [ Links ]

7. Johnson, N., Kotz, S. & Balakrishnan, N. (1994), Continuous univariate distributions, Wiley.         [ Links ]

8. Lawless, J. F. (1982), Statistical model and methods for lifetime data, Wiley, New York.         [ Links ]

9. Liese, F. & Vajda, I. (2006), 'On divergences and informations in statistics and information theory', IEEE Transactions on Information Theory 52, 4394-4412.         [ Links ]

10. Mahdizadeh, M. (2012), 'On the use of ranked set samples in entropy based test of fit for the Laplace distribution', Revista Colombiana de Estadística 35(3), 443-455.         [ Links ]

11. Siddiqui, M. (1962), 'Some problems connected with Rayleigh distribution', Journal of Research of the National Bureau of Standards 66D, 167-174.         [ Links ]

12. Soliman, A. & Al-Aboud, F. M. (2008), 'Bayesian inference using record values from Rayleigh model with application', European Journal of Operational Research 185, 659-672.         [ Links ]

13. Zamanzade, E. & Mahdizadeh, M. (2017), 'Entropy estimation from ranked set samples with application to test of fit', Revista Colombiana de Estadística 40(2), 223-241.         [ Links ]

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