Journal of the Iranian Statistical Society

On Burr III-Inverse Weibull Distribution with COVID-19 Applications

Authors

1 National College of Business Administration and Economics, Lahore, PAKISTAN

2 St. Jude Children’s Research Hospital, Memphis, TN, USA

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

10.52547/jirss.20.1.101

Abstract

We introduce a flexible lifetime distribution called Burr III-Inverse Weibull (BIII-IW). The new proposed distribution has well-known sub-models. The BIII-IW density function includes exponential, left-skewed, right-skewed and symmetrical shapes. The BIII-IW model’s failure rate can be monotone and non-monotone depending on the parameter values. To show the importance of the BIII-IW distribution, we establish various mathematical properties such as random number generator, ordinary moments, conditional moments, residual life functions, reliability measures and characterizations. We address the maximum likelihood estimates (MLE) for the BIII-IW parameters and estimate the precision of the maximum likelihood estimators via a simulation study. We consider applications to two COVID-19 data sets to illustrate the potential of the BIII-IW model.

Keywords

  1. Abbas, S., Hameed, M., Cakmakyapan, S., and Malik, S. (2020), On gamma inverse Weibull distribution. Journal of the National Science Foundation of Sri Lanka, 47(4), 445-453.
  2. Abbas, S., Taqi, S., Mustafa, F., Murtaza, M., and Shahbaz, M. (2017), Topp-Leone Inverse Weibull Distribution: Theory and Application.European Journal of Pure and Applied Mathematics, 10(5), 1005-1022.
  3. Alzaatreh, A., Mansoory, M., Tahirz, M. H., Zubair, M., and Ghazalik, S. A. (2016), The gamma half-Cauchy distribution: Properties and applications. Hacettepe Journal of Mathematics and Statistics, 45(4), 1143-1159.
  4. Alzaatreh, A., Lee, C., and Famoye, F. (2013), A new method for generating families of continuous distributions. Metron, 71(1), 63-79. [DOI:10.1007/s40300-013-0007-y]
  5. Bantan, R. A., Chesneau, C., Jamal, F., and Elgarhy, M. (2020), On the Analysis of New COVID-19 Cases in Pakistan Using an Exponentiated Version of the M Family of Distributions. Mathematics, 8(6), 953.
  6. Bhattacharyya, G. K., and Johnson, R. A. (1974), Estimation of reliability in a multicomponent stress-strength model. Journal of the American Statistical Association, 69(348), 966-970. [DOI:10.1080/01621459.1974.10480238]
  7. Elbatal, I., Condino, F., and Domma, F. (2016), Reflected generalized beta inverse Weibull distribution: definition and properties. Sankhya B, 78(2), 316-340. [DOI:10.1007/s13571-015-0114-2]
  8. Eliwa, M. S., El-Morshedy, M., and Ali, S. (2020), Exponentiated odd Chen-G family of distributions: statistical properties, Bayesian and non-Bayesian estimation with applications. Journal of Applied Statistics, 1-27. [DOI:10.1080/02664763.2020.1783520]
  9. Fayomi, A. (2019). The odd Frechet inverse Weibull distribution with application. Journal of Nonlinear Sciences and Applications, {bf 12, 165-172.
  10. Glanzel W. A. (1987). Characterization theorem based on truncated moments and its application to some distribution families. Mathematical Statistics and Probability Theory (Bad Tatzmannsdorf, 1986), Vol. B, Reidel, Dordrecht, 75-84. [DOI:10.1007/978-94-009-3965-3_8]
  11. Hafida G. and Haitham Y. H. (2019), 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. Khan, M. S. (2010), The beta inverse Weibull distribution. International Transactions in Mathematical Sciences and Computer, 3(1), 113-119.
  13. Khan, M. S., and King, R. (2016), New generalized inverse Weibull distribution for lifetime modeling. Communications for Statistical Applications and Methods, 23(2), 147-161. [DOI:10.5351/CSAM.2016.23.2.147]
  14. Keller, A.Z. and Kamath, A.R.R. (1982), Alternative Reliability Models for Mechanical Systems. Proceeding of the 3rd International Conference on Reliability and Maintainability, 411-415.
  15. Kotz S., Lai CD and Xie M. (2003), On the Effect of Redundancy for Systems with Dependent Components. IIE Transactions, 35(12), 1103-1110. [DOI:10.1080/714044440]
  16. Eliwa M. S. , El-Morshedy M. and Ali S., (2020), Exponentiated odd Chen-G family of distributions: statistical properties, Bayesian and non-Bayesian estimation with applications. Journal of Applied Statistics. [DOI:10.1080/02664763.2020.1783520]
  17. Shahbaz, M. Q., Shahbaz, S., and Butt, N. S. (2012), The Kumaraswamy-Inverse Weibull Distribution. Pakistan Journal of Statistics and Operation Research, 8(3), 479-489. [DOI:10.18187/pjsor.v8i3.520]
Journal of the Iranian Statistical Society
Volume 20, Issue 1
June 2021
Pages 101-121
  • Receive Date: 23 July 2022
  • Revise Date: 20 May 2024
  • Accept Date: 23 July 2022