217
Views
4
CrossRef citations to date
0
Altmetric
Articles

On estimation of the PDF and the CDF of the one-parameter polynomial exponential family of distributions

, &
Pages 104-120 | Received 10 Aug 2020, Accepted 24 Mar 2021, Published online: 26 Apr 2021

References

  • Alizadeh, M., S. Rezaei, S. F. Bagheri, and S. Nadarajah. 2015. Efficient estimation for the generalized exponential distribution. Statistical Papers 56 (4):1015–31. doi: 10.1007/s00362-014-0621-7.
  • Asrabadi, B. R. 1990. Estimation in the Pareto distribution. Metrika 37 (1):199–205. doi:10.1007/BF02613522.
  • Ayesha, A. 2017. Size biased Lindley distribution and its properties a special case of weighted distribution. Applied Mathematics 08 (06):808–19. doi:10.4236/am.2017.86063.
  • Bagheri, S. F., M. Alizadeh, J. E. Baloui, and S. Nadarajah. 2014. Evaluation and comparison of estimations in the generalized exponential-Poisson distribution. Journal of Statistical Computation and Simulation 84 (11):2345–60. doi:10.1080/00949655.2013.793342.
  • Bagheri, S. F., M. Alizadeh, and S. Nadarajah. 2016a. Efficient estimation of the PDF and the CDF of the exponentiated Gumbel distribution. Communications in Statistics - Simulation and Computation 45 (1):339–61. doi:10.1080/03610918.2013.863922.
  • Bagheri, S. F., M. Alizadeh, S. Nadarajah, and E. Deiri. 2016b. Efficient estimation of the PDF and the CDF of the Weibull extension model. Communications in Statistics - Simulation and Computation 45 (6):2191–207. doi:10.1080/03610918.2014.894059.
  • Bakouch, H. S., M. B. Al-Zahrani, A. A. Al-Shomrani, A. A. V. Marchi, and F. Louzada. 2012. An extended Lindley distribution. Journal of the Korean Statistical Society 41 (1):75–85. doi:10.1016/j.jkss.2011.06.002.
  • Bjerkedal, T. 1960. Acquisition of resistance in guinea pigs infected with different doses of virulent tubercle bacilli. American Journal of Hygiene 72 (1):130–48. doi:10.1093/oxfordjournals.aje.a120129.
  • Bouchahed, L., and H. Zeghdoudi. 2018. A new and unified approach in generalizing the Lindley’s distribution with applications. Statistics in Transition New Series 19 (1):61–74. doi:10.21307/stattrans-2018-004.
  • Dixit, U. J., and N. M. Jabbari. 2010. Efficient estimation in the Pareto distribution. Statistical Methodology 7 (6):687–91. doi:10.1016/j.stamet.2010.04.002.
  • Dixit, U. J., and N. M. Jabbari. 2011. Efficient estimation in the Pareto distribution with the presence of outliers. Statistical Methodology 8 (4):340–55. doi:10.1016/j.stamet.2011.01.011.
  • Elbatal, I., F. Merovci, and M. Elgarhy. 2013. A new generalized Lindley distribution. Mathematical Theory and Modeling 3 (13):30–47.
  • Ghitany, E. M., K. D. Al-Mutairi, N. Balakrishnan, and J. L. Al-Enezi. 2013. Power Lindley distribution and associated inference. Computational Statistics & Data Analysis 64:20–33. doi:10.1016/j.csda.2013.02.026.
  • Gross, A. J., and V. A. Clark. 1975. Survival distributions: Reliability Applications in the Biometrical Sciences. New York: John Wiley.
  • Jabbari, N. M., and N. H. Jabbari. 2010. Efficient estimation of PDF, CDF and rth moment for the exponentiated Pareto distribution in the presence of outliers. Statistics: A Journal of Theoretical and Applied Statistics 44 (4):1–20.
  • Kumar, P., K. Kour, and J. Kour. 2018. Estimation of the probability density function of Lomax distribution. International Journal of Statistics and Economics 19 (2):78–88.
  • Lawless, J. F. 1982. Statistical models and methods for lifetime data. Hoboken, NJ: John Wiley & Sons, Inc.
  • Lindley, D. V. 1958. Fiducial distributions and Bayes’ theorem. Journal of the Royal Statistical Society: Series B (Methodological) 20 (1):102–7. doi:10.1111/j.2517-6161.1958.tb00278.x.
  • Maiti, S. S., and I. Mukherjee. 2018. On estimation of the PDF and CDF of the Lindley distribution. Communications in Statistics - Simulation and Computation 47 (5):1370–81. doi:10.1080/03610918.2017.1311919.
  • Mukherjee, I., S. Dey, and S. S. Maiti. 2016. Comparison of estimators of the PDF and CDF of the generalized exponential distribution. Proceedings of Institute for Mathematics, Bio-informatics, Information-technology and Computer-Science, Vol. 5, pp. 266–81.
  • Mukherjee, I., and S. S. Maiti. 2019. A note on estimation of the PDF and CDF of the lognormal distribution. Proceedings of Institute for Mathematics, Bio-Informatics, Information-Technology and Computer-Science Vol. 8, pp. 163–74.
  • Rasheki, M. 2018. A study on methods for estimating the pdf and the cdf in the exponentiated gamma distribution. Communications in Statistics - Simulation and Computation 49 (8):1999–2013.
  • Shanker, R. 2015. Akash distribution and its applications. International Journal of Probability and Statistics 4 (3):65–75.
  • Shanker, R. 2016a. Amarendra distribution and its applications. American Journal of Mathematics and Statistics 6 (1):44–56.
  • Shanker, R. 2016b. Aradhana distribution and its applications. International Journal of Statistics and Applications 6 (1):23–34.
  • Shanker, R. 2016c. Devya distribution and its applications. International Journal of Statistics and Applications 6 (4):189–202.
  • Shanker, R. 2016d. Shambhu distribution and its applications. International Journal of Probability and Statistics 5 (2):48–63.
  • Shanker, R. 2016e. Sujatha distribution and its applications. Statistics in Transition. New Series 17 (3):391–410. doi:10.21307/stattrans-2016-029.
  • Shanker, R., and A. H. Ghebretsadik. 2013. A new quasi Lindley distribution. International Journal of Statistics and Systems 8 (2):143–56.
  • Singh, Y. 2012. Unbiased estimation in burr distribution. Journal of Mathematical and Computational Science 2 (4):830–5.
  • Torkaman, P. 2020. Evaluation for estimating of the pdf and the cdf of generalized inverted exponential distribution with application in industry. Advances in Mathematics: Scientific Journal 9 (1):507–22.
  • Tripathi, Y. M., T. Kayal, and S. Dey. 2017a. Estimation of the PDF and the CDF of a exponentiated moment exponential distribution. International Journal of System Assurance Engineering and Management 8 (S2):1282–96. doi:10.1007/s13198-017-0599-3.
  • Tripathi, Y. M., A. K. Mahto, and S. Dey. 2017b. Efficient estimation of the PDF and the CDF of a generalized logistic distribution. Annals of Data Science 4 (1):63–81. doi:10.1007/s40745-016-0093-9.
  • Zakerzadeh, H., and A. Dolati. 2009. Generalized Lindley distribution. Journal of Mathematical Extension 3 (2):1–17.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.