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Abstract

We introduce a four-parameter lifetime model with flexible hazard rate called the Burr XII gamma (BXIIG) distribution.  We derive the BXIIG distribution from (i) the T-X family technique and (ii) nexus between the exponential and gamma variables. The failure rate function for the BXIIG distribution is flexible as it can accommodate various shapes such as increasing, decreasing, decreasing-increasing, increasing-decreasing-increasing, bathtub and modified bathtub.  Its density function can take shapes such as exponential, J, reverse-J, left-skewed, right-skewed and symmetrical. To illustrate the importance of the BXIIG distribution, we establish various mathematical properties such as random number generator, ordinary moments, generating function, conditional moments, density functions of record values, reliability measures and characterizations.  We address the maximum likelihood estimation for the parameters. We estimate the adequacy of the estimators via a simulation study. We consider applications to two real data sets to prove empirically the potentiality of the proposed model.

Keywords

Characterizations Gamma distribution Maximum Likelihood Estimation Reliability

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Author Biographies

Fiaz Ahmad Bhatti, National College of Business Administration and Economics , Lahore Pakistan

Deptt. of Statistics, Ph.D. Scholar

Gauss, Departamentode Estatística, Universidade Federal de Pernambuco, Recife, PE, Brazil

Departamentode Estatística, Universidade Federal de Pernambuco, Recife, PE, Brazil

Korkmaz, Department of Measurement and Evaluation, Artvin Çoruh University, Artvin, Turkey

Department of Measurement and Evaluation, Artvin Çoruh University, Artvin, Turkey

Hamedani, Marquette University, Milwaukee, WI 53201-1881, USA

Marquette University, Milwaukee, WI 53201-1881, USA

How to Cite
Bhatti, F. A., Cordeiro, G. M., Korkmaz, M. Ç., & Hamedani, G. (2021). On The Burr XII-Gamma Distribution: Development, Properties, Characterizations and Applications: Burr XII Gamma Distribution. Pakistan Journal of Statistics and Operation Research, 17(4), 771-789. https://doi.org/10.18187/pjsor.v17i4.3453
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References

  1. Alzaatreh, A., Mansoor, M., Tahir, M. H., Zubair, M., & Ali, S. (2016). The Gamma Half-Cauchy Distribution: Properties and Applications. Hacettepe Journal of Mathematics and Statistics, 45, 1143 -1159.
  2. Bhatti, F. A., Hamedani, G. G., Korkmaz, M. Ç., Sheng, W., & Ali, A. (2021). On the Burr XII-moment exponential distribution. Plos one, 16(2), e0246935
  3. Bhatti, F. A., Hamedani, G. G., Al Sobhi, M. M., & Korkmaz, M. Ç. (2021). On the Burr XII-Power Cauchy distribution: Properties and applications. AIMS Mathematics, 6(7), 7070-7092
  4. Bjerkedal, T. (1960). Acquisition of Resistance in Guinea Pies infected with Different Doses of Virulent Tubercle Bacilli. American Journal of Hygiene, 72, 130-148.
  5. Burr, I. W. (1942). Cumulative frequency functions. The Annals of mathematical statistics, 13(2), 215-232
  6. Cordeiro, G. M., & de Castro, M. (2011). A new family of generalized distributions. Journal of statistical computation and simulation, 81, 883-898.
  7. Cordeiro, G. M., Bourguignon, M., Ortega, E. M., & Ramires, T. G. (2018). General mathematical properties, regression and applications of the log-gamma-generated family. Communications in Statistics-Theory and Methods, 47, 1050-1070.
  8. Flajolet, P., & Odlyzko, A. (1990). Singularity analysis of generating functions. SIAM Journal on discrete mathematics, 3(2), 216-240.
  9. Flajolet, P., & Sedgewick, R. (2009). Analytic combinatorics. Cambridge University press.
  10. Glänzel, W. A. (1990). Some consequences of a characterization theorem based on truncated moments, Statistics, 21, 613 - 618.
  11. Goual, H., & Yousof, H. M. (2020). Validation of Burr XII inverse Rayleigh model via a modified chi-squared goodness-of-fit test. Journal of Applied Statistics, 47(3), 393-423
  12. Gradshteyn, I. S., & Ryzhik, I. M. (2000). Table of integrals, series, and products 6th edn (san diego, ca: Academic)
  13. Gupta, R. C., Kannan, N. and Raychaudhuri, A. (1997). Analysis of lognormal survival data. Math. Biosci. 139, 103-115.
  14. Haghbin, H., Ozel, G., Alizadeh, M., & Hamedani, G. G. (2017). A new generalized odd log-logistic family of distributions. Communications in Statistics-Theory and Methods, 46, 9897-9920.
  15. Kong, L., Lee, C., & Sepanski, J. H. (2007). On the properties of beta-gamma distribution. Journal of Modern Applied Statistical Methods, 6, 18.
  16. Korkmaz, M. Ç (2017). A generalized skew slash distribution via gamma-normal distribution. Communications in Statistics-Simulation and Computation, 46, 1647-1660.
  17. Kotz S, Lai CD, Xie M. (2003). â€On the Effect of Redundancy for Systems with Dependent Components.†IIE Trans, 35, 1103-1110.
  18. Lee, E. T. and Wang, J. W. (2003). Statistical Methods for Survival Data Analysis, 3rd ed., Wiley, New York.
  19. Lemonte, A. J. and Cordeiro, G. M. (2013). An extended Lomax distribution. Statistics, 47, 800-816.
  20. Mdlongwa, P., Oluyede, B., Amey, A., & Huang, S. (2017). The Burr XII modified Weibull distribution: model, properties and applications. Electronic Journal of Applied Statistical Analysis, 10(1), 118-145
  21. Nasir, M. A., Özel, G., & Jamal, F. (2018). The Burr Xii Uniform Distribution: Theory And Applications. Journal of Reliability and Statistical Studies, 143-158
  22. Rezaei, S., Sadr, B. B., Alizadeh, M., & Nadarajah, S. (2017). Topp-Leone generated family of distributions: Properties and applications. Communications in Statistics-Theory and Methods, 46, 2893-2909.