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Abstract





The current paper presented new two-parameter life processes distribution, the Marshall-Olkin Pranav (MOEP) distribution. This study combines the Marshall-Olkin method with the Pranav distribution to produce a more accessible and flexible model used to perform data survival techniques. Some of its critical statistical features are presented in this study. For instance, we mentioned its survival , hazard, reversed hazard, and cumulative hazard rate function. Then we discussed its Moment generating functions, The characteristic function, Incomplete moments, R`enyi and Entropies, and stochastic orderings. The research utilized maximization of chance in estimating parameters. These tests are done through simulations to achieve the desired results. After its attainment, real-life data was used to test the new model, which possesses the best goodness of fit.





Keywords

Marshall-Olkin family of distribution Pranav distribution Stochastic ordering Maximum likelihood Quantile incomplet moments Generating function

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How to Cite
Alsultan, R. (2023). The Marshall-Olkin Pranav distribution: Theory and applications. Pakistan Journal of Statistics and Operation Research, 19(1), 155-166. https://doi.org/10.18187/pjsor.v19i1.4058
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References

  1. Ahmad, Z. (2020). The zubair-G family of distributions: properties and applications. Annals of Data Science, 7(2):195–208. https://doi.org/10.1007/s40745-018-0169-9
  2. Asgharzadeh, A., Bakouch, H. S., Nadarajah, S., & Sharafi, F. (2016). A new weighted lindley distribution with application. Brazilian Journal of Probabil- ity and Statistics, 30(1):1–27. DOI: 10.1214/14-BJPS253
  3. Bjerkedal, T. et al. (1960). Acquisition of resistance in guinea pies infected with different doses of virulent tubercle bacilli. American Journal of Hygiene, 72(1):130–48. DOI: 10.1093/oxfordjournals.aje.a120129
  4. Cordeiro, G.M.,& Lemonte, A.J.,( 2013). On the Marshall-Olkin extended Weibull distribution. Statistical papers. 54, 333-353. DOIhttps://doi.org/10.1007/s00362-012-0431-8
  5. Chipepa, F., Moakofi, T., & Oluyede, B. (2022). The Marshall-Olkin-Odd Power Generalized Weibull-G Family of Distributions with Applications of COVID-19 Data. Journal of Probability and Statistical Science, 20(1), 1-20. DOI: https://doi.org/10.37119/jpss2022.v20i1.509
  6. Eugene, N., Lee, C., & Famoye, F. (2002). Beta-normal distribution and its applications. Communications in Statistics-Theory and methods, 31(4):497– 512. https://doi.org/10.1081/STA-120003130
  7. Fuller Jr, E. R., Freiman, S. W., Quinn, J. B., Quinn, G. D., & Carter, W. C. (1994). Fracture mechanics approach to the design of glass aircraft windows: A case study. In Window and dome technologies and materials IV, volume 2286, pages 419–430. International Society for Optics and Photonics. https://doi.org/10.1117/12.187363
  8. Granzotto, D., Louzada, F., & Balakrishnan, N. (2017). Cubic rank trans- muted distributions: inferential issues and applications. Journal of statistical Computation and Simulation, 87(14):2760–2778. https://doi.org/10.1080/00949655.2017.1344239
  9. Javed, M., Nawaz, T., & Irfan, M. (2019). The Marshall-Olkin kappa distribution: properties and applications. Journal of King Saud University-Science, 31(4), 684-691. https://doi.org/10.1016/j.jksus.2018.01.001
  10. KK, S. (2018). Pranav distribution with properties and its applications. Biom Biostat Int J, 7(3):244–254. DOI: 10.15406/bbij.2018.07.00215
  11. Kumaraswamy, P. (1980). A generalized probability density function for double- bounded random processes. Journal of hydrology, 46(1-2):79–88. https://doi.org/10.1016/0022-1694(80)90036-0
  12. Mahdavi, A. & Kundu, D. (2017). A new method for generating distributions with an application to exponential distribution. Communications in Statistics-Theory and Methods, 46(13):6543–6557. https://doi.org/10.1080/03610926.2015.1130839
  13. 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. https://doi.org/10.1093/biomet/84.3.641
  14. Moakofi, T., Oluyede, B., & Makubate, B. (2021). Marshall-Olkin Lindley-Log-logistic distribution: Model, properties and applications. Mathematica Slovaca, 71(5), 1269-1290. https://doi.org/10.1515/ms-2021-0052
  15. Mudholkar, G. S. & Srivastava, D. K. (1993). Exponentiated weibull family for analyzing bathtub failure-rate data. IEEE transactions on reliability, 42(2):299–302. DOI: 10.1109/24.229504
  16. Rahman, M. M., Al-Zahrani, B., & Shahbaz, M. Q. (2018). A general trans- muted family of distributions. Pakistan Journal of Statistics and Operation Research, pages 451–469. https://doi.org/10.18187/pjsor.v14i2.2334
  17. Shaked, M. & Shanthikumar, J. G. (2007). Stochastic orders. New York, Ny: Springer New York. https://doi.org/10.1007/978-0-387-34675-5_1
  18. Shanker, R. and Mishra, A. (2013). A quasi Lindley distribution. African Journal of Mathematics and Computer Science Research, 6(4), 64-71. DOI 10.5897/AJMCSR 12.067
  19. Shaw, W. T. & Buckley, I. R. (2009). The alchemy of probability distributions: beyond gram-charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map. arXiv preprint arXiv:0901.0434. https://doi.org/10.48550/arXiv.0901.0434