Main Article Content


A new generalization of generalized Pareto Distribution is obtained using the generator Marshall-Olkin distribution (1997). The new distribution MOGP is more flexible and can be used to model non-monotonic failure rate functions. MOGP includes six different sub models: Generalized Pareto, Exponential, Uniform, Pareto type I, Marshall-Olkin Pareto and Marshall-Olkin exponential distribution. We consider different estimation procedures for estimating the model parameters, namely: Maximum likelihood estimator, Maximum product spacing, Least square method, weighted least square method and Bayesian Method. The Bayesian Method is considered under quadratic loss function and Linex loss function. Simulation analysis using MCMC technique is performed to compare between the proposed point estimation methods. The usefulness of MOGP is illustrated by means of real data set, which shows that this generalization is better fit than Pareto, GP and MOP distributions.


Marshall-Olkin distribution Generalized Pareto distribution Maximum Product Spacing Bayes estimation Monte Carlo simulations.

Article Details

Author Biographies

Hanan Haj AHmad, King Faisal University

Basic Science department , Assistant Professor.

Ehab Almetwally, Institute of Statistical Studies and Research, Cairo University, Cairo, Egypt

Institute of Statistical Studies and Research

How to Cite
Haj AHmad, H., & Almetwally, E. (2020). Marshall-Olkin Generalized Pareto Distribution: Bayesian and Non Bayesian Estimation. Pakistan Journal of Statistics and Operation Research, 16(1), 21-33.


  1. Alice, T. & Jose, K. K. (2004). Marshall-Olkin exponential time series modeling. STARS International Journal 5(1):12-22.
  2. Almetwally, E. M., & Almongy, H. M. (2019 a). Maximum Product Spacing and Bayesian Method for Parameter Estimation for Generalized Power Weibull Distribution under Censoring Scheme. Journal of Data Science, 17(2), 407-444.
  3. Almetwally, E. M., & Almongy, H. M. (2019 b). Estimation Methods for the New Weibull-Pareto Distribution: Simulation and Application. Journal of Data Science, 17(3), 610-630.‏
  4. Almetwally, E. M., Almongy, H. M., & El sayed Mubarak, A. (2018). Bayesian and Maximum Likelihood Estimation for the Weibull Generalized Exponential Distribution Parameters Using Progressive Censoring Schemes. Pakistan Journal of Statistics and Operation Research, 14(4), 853-868.
  5. Almetwaly, E. M., & Almongy, H. M. (2018). Estimation of the Generalized Power Weibull Distribution Parameters Using Progressive Censoring Schemes. International Journal of Probability and Statistics, 7(2), 51-61.
  6. Basheer, A. M. (2019). Marshall-Olkin alpha power inverse exponential distribution: properties and applications, Annals of data science,, (2019).
  7. Bdair, O. & Haj Ahmad, H. (2019). Estimation of the Marshall-Olkin Pareto Distribution Parameters: Comparative Study. REVISTA INVESTIGACION OPERACIONAL, 41(2), forthcoming.
  8. Birnbaum, Z. W., & Saunders, S. C. (1969). Estimation for a family of life distributions with applications to fatigue. Journal of Applied Probability, 6(2), 328-347.
  9. Castillo, E., Hadi, A. S., Balakrishnan, N. & Sarabia, J. M. (2005). Extreme Value and Related Models with Applications in Engineering and Science. Hoboken, NJ: Wiley. MR2191401
  10. Cheng, R. C. H. & Amin, N. A. K. (1983). Estimating parameters in continuous univariate distributions with a shifted origin. J. Roy. Statist.Soc. Ser. B, 45, 394 - 403.
  11. El-Sherpieny, E. S. A., Almetwally, E. M., & Muhammed, H. Z. (2020). Progressive Type-II hybrid censored schemes based on maximum product spacing with application to Power Lomax distribution. Physica A: Statistical Mechanics and its Applications, 124251.‏
  12. Ghitany, M.E. (2005) Marshall-Olkin extended Pareto distribution and its application. International Journal of Applied Mathematics, 18, No.1, 17-31.
  13. Gupta, R.C., Gupta, R.D. & Gupta, P.L. (1998). Modeling failure time data by Lehman alternatives. Communications in Statistics: Theory and Methods, 27, 887-904.
  14. Haj Ahmad, H., Bdair, O. & Ahsanullah, M. (2017). On Marshall-Olkin Extended Weibull Distribution. Journal of Statistical Theory and Applications, Vol. 16, No. 1, 1–17
  15. Hogg, R.V., McKean, J.W. & Craig, A.T. (2005). Introduction to Mathematical Statistics, 6th ed. Pearson Prentice-Hall, New Jersey, 2005.
  16. Jose, K.K. (2011). Marshall-Olkin Family of Distributions and their applications in reliability theory, time series modeling and stress-strength analysis. int. statistical inst. proc 58th world statistical congress, Dublin (Session CPS 005).
  17. Jose, K. K. & Alice, T. (2001) Marshall-Olkin Generalized Weibull distributions and applications, STARS: int. Journal, 2, 1, 1-8.
  18. Jose, K. K. & Alice, T. (2005) Marshall-Olkin Family of Distributions: Applications in Time series modelling and Reliability, J.C Publications, Palakkad.
  19. Jose, K. K. & Uma, P. (2009) On Marshall-Olkin Mittag-Leffler distributions and processes, Far East Journal of Theoretical Statistics, 28,189-199.
  20. Karian, Z. A. & Dudewicz, E. J. (1999). Modern Statistical Systems and GPSS Simulations, 2nd edition, CRC Press, Florida.
  21. KARANDIKAR, R.L. (2006). On Markov Chain Monte Carlo (MCMC) Method, Sadhana, 31, 81-104.
  22. Kotz, S. & Nadarajah, S. (2000) Extreme Value Distributions: Theory and Applications. Imperial College Press, London.
  23. Marshall, A. W. & 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.
  24. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M., Teller, A. H. & Teller, E. (1953). Equation of State Calculations by Fast Computing Machines, The Journal of Chemical Physics, 21, 1087; doi: 10.1063/1.1699114
  25. Okasha, H. M., El-Baz, A. H. & Basheer A. M., (2020). On Marshall-Olkin extended inverse Weibull distribution: properties and estimation using type-II censoring data, Journal of Statistics Applications & Probability Letters, 7(1), 9-21.
  26. Pickands, J. (1975). Statistical inference using extreme order statistics. Annals of Statistics, 3, 119--131.
  27. Robert, C.P. & Casella, G. (2004). Monte Carlo Statistical Methods. Springer, New York.
  28. Sankaran, P. G. & Jayakumar, K. (2006). On proportional odds model, Statistical Papers 49, 779-789.
  29. Singh, U., Singh, S. K., & Singh, R. K. (2014). A comparative study of traditional estimation methods and maximum product spacing method in generalized inverted exponential distribution. Journal of Statistics Applications & Probability, 3(2), 153.
  30. Swain, J., Venkatraman, S. & Wilson, J. (1988). Least Squares Estimation of Distribution Function in Johnson's Translation System, Journal of Statistical Computation and Simulation 29, 271-297.