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The main motivation of this paper is to show how the different frequentist estimators of the new distribution perform for different sample sizes and different parameter values and to raise a guideline in choosing the best estimation method for the new model. The unknown parameters of the new distribution are estimated using the maximum likelihood method, ordinary least squares method, weighted least squares method, Cramer-Von-Mises method and Bayesian method. The obtained estimators are compared using Markov Chain Monte Carlo simulations and we observed that Bayesian estimators are more efficient compared to other the estimators.


Different Method of Estimations Markov Chain Monte Carlo Simulations Clayton Copula Bayesian Estimation Farlie Gumbel Morgenstern Copula Renyi's entropy Copula

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Ibrahim, M., Mohammed, W., & Yousof, H. M. (2020). Bayesian and Classical Estimation for the One Parameter Double Lindley Model. Pakistan Journal of Statistics and Operation Research, 16(3), 409-420.


  1. Afify, A. Z., Cordeiro, G. M., Nadarajah, S., Yousof, H. M., Ozel, G., Nofal, Z. M. and Emrah Altun. (2018a). The complementary geometric transmuted-G family of distributions: model, properties and applications. Austrian Journal of Statistics, 47, 51-71.
  2. Afify, A. Z., Cordeiro, G. M., Yousof, H. M., Saboor, A. and Ortega, E. M. (2018b). The Marshall-Olkin additive Weibull distribution with variable shapes for the hazard rate. Hacettepe J Math Stat, 47, 365-381.‏
  3. Afify, A. Z., Yousof, H. M., and Nadarajah, S. (2017). The beta transmuted-H family of distributions: properties and applications. Stasistics and its Inference, 10, 505--520.
  4. Alizadeh, M., Rasekhi, M., Yousof, H. M. and Hamedani G. G. (2018). The transmuted Weibull G family of distributions. Hacettepe Journal of Mathematics and Statistics, 47(6), 1-20.
  5. Alizadeh, M., Yousof, H. M., Afify, A. Z., Cordeiro, G.M. and Mansoor, M. (2016). The complementary generalized transmuted Poisson-G family of distributions. Austrian Journal of Statistics, forthcoming.
  6. Bakouch, H. S., Al-Zaharani, B., Al-Shomrani, A., Marchi, V., Louzad, F. (2012). An extended Lindley distribution. Journal of the Korean Statistical Society, 41, 75-85.
  7. Cordeiro, G. M., Afify, A. Z., Yousof, H. M., Pescim, R. R. and Aryal, G. R. (2017). The exponentiated Weibull-H family of distributions: Theory and Applications. Mediterranean Journal of Mathematics, 14, 1-22.
  8. Deniz, E. and Ojeda, E. (2011). The discrete Lindley distribution-Properties and Applications. Journal of Statistical Computation and Simulation, 81, 1405-1416.
  9. Farlie, D. J. G. (1960) The performance of some correlation coefficients for a general bivariate distribution. Biometrika, 47, 307-323.
  10. Goual, H., Yousof, H. M. and Ali, M. M. (2019). Validation of the odd Lindley exponentiated exponential by a modified goodness of fit test with applications to censored and complete data. Pakistan Journal of Statistics and Operation Research. 15(3), 745-771.
  11. Gumbel, E. J. (1961). Bivariate logistic distributions. Journal of the American Statistical Association, 56(294), 335-349.
  12. Gumbel, E. J. (1960) Bivariate exponential distributions. Journ. Amer. Statist. Assoc., 55, 698-707.
  13. Ghitany, M. E., Al-Mutairi, D. K. and Nadarajah, S. (2008a). Zero-truncated Poisson--Lindley distribution and its application. Mathematics and Computers in Simulation, 79, 279-287.
  14. Ghitany, M. E., Atieh, B. and Nadarajah, S. (2008b). Lindley distribution and its application. Mathematics and computers in simulation, 78, 493-506.
  15. Ghitany, M. E., Alqallaf , F., Al-Mutairi, D. K., and Husain, H. A., (2011) A two-parameter weighted Lindley distribution and its applications to survival data, Mathematics and Computers in Simulation, 81,1190-1201.
  16. Ibrahim, M. (2019). A new extended Fréchet distribution: properties and estimation. Pak. J. Stat. Oper. Res.,15 (3), 773-796.
  17. Ibrahim, M. (2020a). The compound Poisson Rayleigh Burr XII distribution: properties and applications. Journal of Applied Probability and Statistics, 15(1), 73-97.
  18. Ibrahim, M. (2020b). The generalized odd Log-logistic Nadarajah Haghighi distribution: statistical properties and different methods of estimation. Journal of Applied Probability and Statistics, forthcoming.
  19. Ibrahim, M., Altun, E. and Yousof, H. M. (2020). A new distribution for modeling lifetime data with different methods of estimation and censored regression modeling. Statistics, Optimization and Information Computing, 8, 610–630.
  20. Ibrahim, M., Yadav, A. S. Yousof, H. M., Goual, H. and Hamedani, G. G. (2019). A new extension of Lindley distribution: modified validation test, characterizations and different methods of estimation, Communications for Statistical Applications and Methods, 26(5), 473–495.
  21. Korkmaz, M. Ç., Alizadeh, M., Yousof, H. M., & Butt, N. S. (2018a). The generalized odd Weibull generated family of distributions: statistical properties and applications. Pakistan Journal of Statistics and Operation Research, 14(3), 541-556.‏
  22. Korkmaz, M. C., Altun, E., Yousof, H. M. and Hamedani G. G. (2019). The odd power Lindley generator of probability distributions: properties, characterizations and regression modeling, International Journal of Statistics and Probability, 8(2), 70-89.
  23. Korkmaz, M. C. Yousof, H. M. and Ali, M. M. (2017). Some theoretical and computational aspects of the odd Lindley Fréchet distribution, Journal of Statisticians: Statistics and Actuarial Sciences, 2, 129-140.
  24. Korkmaz, M. C. Yousof, H. M. and Hamedani G. G. (2018b). The exponential Lindley odd log-logistic G family: properties, characterizations and applications. Journal of Statistical Theory and Applications, 17(3), 554 - 571.
  25. Lindley, D.V. (1958). Fiducial distributions and Bayes' theorem. Journal of the Royal Statistical Society. Series B (Methodological), 102-107.
  26. Merovci, F., Alizadeh, M., Yousof, H. M. and Hamedani G. G. (2017). The exponentiated transmuted-G family of distributions: theory and applications, Communications in Statistics-Theory and Methods, 46(21), 10800-10822.
  27. Merovci, F. and Sharma, V. K. (2014). The beta Lindley distribution: Properties and applications. Journal of Applied Mathematics, ID 198951, 1-10.
  28. Merovci, F., Yousof, H. and Hamedani, G. G. (2020). The Poisson Topp Leone Generator of Distributions for Lifetime Data: Theory, Characterizations and Applications. Pakistan Journal of Statistics and Operation Research, 16(2), 343-355.‏
  29. Mansour, M., Yousof, H. M., Shehata, W. A. M. and Ibrahim, M. (2020). A new two parameter Burr XII distribution: properties, copula, different estimation methods and modeling acute bone cancer data, Journal of Nonlinear Science and Applications, 13, 223–238.
  30. Morgenstern, D. (1956). Einfache beispiele zweidimensionaler verteilungen. Mitteilingsblatt fur Mathematische Statistik, 8, 234-235.
  31. Nadarajah, S., Bakouch, H. S. and Tahmasbi, R. (2011). A generalized Lindley distribution. Sankhya B, 73, 331-359.
  32. Nofal, Z. M., Afify, A. Z., Yousof, H. M. and Cordeiro, G. M. (2017). The generalized transmuted-G family of distributions. Communications in Statistics-Theory and Method, 46, 4119-4136.
  33. Ozel, G., Alizadeh, M., Cakmakyapan, S., Hamedani, G. G., Ortega, E. M., & Cancho, V. G. (2017). The odd log-logistic Lindley Poisson model for lifetime data. Communications in Statistics-Simulation and Computation, 46(8), 6513-6537.‏
  34. Pougaza, D. B. and Djafari, M. A. (2011). Maximum entropies copulas. Proceedings of the 30th international workshop on Bayesian inference and maximum Entropy methods in Science and Engineering, 329-336.
  35. Rodriguez-Lallena, J. A. and Ubeda-Flores, M. (2004). A new class of bivariate copulas. Statistics and Probability Letters, 66, 315–25.
  36. Sharma, V., Singh, S., Singh, U. and Agiwal, V. (2015). The inverse Lindley distribution: A stress-strength reliability model with applications to head and neck cancer data. Journal of Industrial & Production Engineering, 32, 162-173.
  37. Silva, F. S., Percontini, A., de Brito, E., Ramos, M. W., Venancio, R. and Cordeiro, G. M. (2017). The Odd Lindley-G Family of Distributions. Austrian Journal of Statistics, 46(1), 65-87.
  38. Singh, S. K., Singh, U., Sharma, V. K. (2014). The Truncated Lindley distribution- inference and Application. J. Stat Appl Pro., 3, 219-228.
  39. Yousof, H. M., Afify, A. Z., Alizadeh, M., Nadarajah, S., Aryal, G. R. and Hamedani, G. G. (2018a). The Marshall-Olkin generalized-G family of distributions with Applications, STATISTICA, 78(3), 273- 295.
  40. Yousof, H. M., Majumder, M., Jahanshahi, S. M. A., Ali, M. M. and Hamedani G. G. (2018b). A new Weibull class of distributions: theory, characterizations and applications, Journal of Statistical Research of Iran, 15, 45–83.