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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.


Marshal-Olkin Extended Rayleigh distribution Goodness of fit Monte-Carlo simulation Asymptotic percentage points Power test

Article Details

Author Biographies

Naz Saud, Lahore College for Women University, Lahore.

Assistant Professor

Sohail Chand, College of Statistical and Actuarial Sciences, University of the Punjab, Quaid-i-Azam Campus, Lahore, Pakistan

Associate Professor

How to Cite
Saud, N., & Chand, S. (2019). Goodness of Fit Tests for Marshal-Olkin Extended Rayleigh Distribution. Pakistan Journal of Statistics and Operation Research, 16(3), 587-598.


  1. Abd-Elfattah, A. (2011). Goodness of fit test for the generalized rayleigh distribution with unknown parameters. Journal of Statistical Computation and Simulation, 81(3):357–366.
  2. Abd-Elfattah, A., Hala, A. F., and Omima, A. (2010). Goodness of fit tests for generalized frechet distribution. Australian Journal of Basic and Applied Sciences, 4(2):286–301.
  3. Al-Zahrani, B. (2012). Goodness-of-fit for the topp-leone distribution with unknown parameters. Applied Mathematical Sciences, 6(128):6355–6363.
  4. Choulakian, V. and Stephens, M. (2001). Goodness-of-fit tests for the generalized pareto distribution. Technometrics, 43(4):478–484.
  5. Cordeiro, G. M. and Lemonte, A. J. (2013). On the marshall–olkin extended Weibull distribution. Statistical Papers, 54(2):333–353.
  6. Gupta, R. D. and Kundu, D. (1999). Generalized exponential distributions. Australian & New Zealand Journal of Statistics, 41(2):173–188.
  7. Hassan, A. S. (2005). Goodness-of-fit for the generalized exponential distribution. Interstat Electronic Journal, pages 1–15.
  8. 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.
  9. Lilliefors, H. W. (1969). On the kolmogorov-smirnov test for the exponential distribution DOI:
  10. with mean unknown. Journal of the American Statistical Association, 64(325):387–389.
  11. 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.
  12. Shin, H., Jung, Y., Jeong, C., and Heo, J.-H. (2011). Assessment of modified anderson–darling test statistics for the generalized extreme value and generalized logistic distributions.Stochastic Environmental Research and Risk Assessment, 26(1):105–114.
  13. 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). Modified goodness-of-fit tests for gamma distributions with unknown location and scale parameters. Reliability, IEEE Transactions on, 33(3):241–245.
  14. Yen, V. C. and Moore, A. H. (1988). Modified goodness-of-fit test for the laplace distribution. Communications in Statistics-Simulation and Computation, 17(1):275–281.
  15. Zainal Abidin, Nahdiya, A. M. B. and Midi, H. (2012). The goodness-of-fit test for gumbel distribution:a comparative study. Matematika, 28(1):3548.