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Abstract
A class of goodness of fit tests for Marshal-Olkin Extended Rayleigh distribution with estimated parameters is proposed. The tests are based on the empirical distribution function. For determination of asymptotic percentage points, Kolomogorov-Sminrov, Cramer-von-Mises, Anderson-Darling,Watson, and Liao-Shimokawa test statistic are used. This article uses Monte Carlo simulations to obtain asymptotic percentage points for Marshal-Olkin extended Rayleigh distribution. Moreover, power of the goodness of fit test statistics is investigated for this lifetime model against several alternatives.
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References
- Abd-Elfattah, A. (2011). Goodness of ï¬t test for the generalized rayleigh distribution with unknown parameters. Journal of Statistical Computation and Simulation, 81(3):357-366.
- Abd-Elfattah, A., Hala, A. F., and Omima, A. (2010). Goodness of ï¬t tests for generalized frechet distribution. Australian Journal of Basic and Applied Sciences, 4(2):286-301.
- Al-Zahrani, B. (2012). Goodness-of-ï¬t for the topp-leone distribution with unknown parameters. Applied Mathematical Sciences, 6(128):6355-6363.
- Choulakian, V. and Stephens, M. (2001). Goodness-of-ï¬t tests for the generalized pareto distribution. Technometrics, 43(4):478-484.
- Cordeiro, G. M. and Lemonte, A. J. (2013). On the marshall-olkin extended Weibull distribution. Statistical Papers, 54(2):333-353.
- Gupta, R. D. and Kundu, D. (1999). Generalized exponential distributions. Australian & New Zealand Journal of Statistics, 41(2):173-188.
- Hassan, A. S. (2005). Goodness-of-ï¬t for the generalized exponential distribution. Interstat Electronic Journal, pages 1-15.
- Lilliefors, H. W. (1967). On the kolmogorov-smirnov test for normality with mean and variance unknown. Journal of the American Statistical Association, 62(318):399-402.
- Lilliefors, H. W. (1969). On the kolmogorov-smirnov test for the exponential distribution
- with mean unknown. Journal of the American Statistical Association, 64(325):387-389.
- Marshall, A. W. and Olkin, I. (1997). A new method for adding a parameter to a family of distributions with application to the exponential and weibull families. Biometrika, 84(3):641-652.
- Shin, H., Jung, Y., Jeong, C., and Heo, J.-H. (2011). Assessment of modiï¬ed anderson-darling test statistics for the generalized extreme value and generalized logistic distributions.Stochastic Environmental Research and Risk Assessment, 26(1):105-114.
- Soetaert, K. (2009). Package rootsolve: roots, gradients and steady-states in r. Woodruff, B. W., Viviano, P. J., Moore, A. H., and Dunne, E. J. (1984). Modiï¬ed goodness-of-ï¬t tests for gamma distributions with unknown location and scale parameters. Reliability, IEEE Transactions on, 33(3):241-245.
- Yen, V. C. and Moore, A. H. (1988). Modiï¬ed goodness-of-ï¬t test for the laplace distribution. Communications in Statistics-Simulation and Computation, 17(1):275-281.
- Zainal Abidin, Nahdiya, A. M. B. and Midi, H. (2012). The goodness-of-ï¬t test for gumbel distribution:a comparative study. Matematika, 28(1):3548.