133
Views
2
CrossRef citations to date
0
Altmetric
Research Articles

A Novel Bivariate Generalized Weibull Distribution with Properties and Applications

, ORCID Icon, ORCID Icon, &

References

  • Almalki, S. J. (2018). A reduced new modified Weibull distribution. Communications in Statistics - Theory and Methods, 47(10), 2297–2313. https://doi.org/10.1080/03610926.2013.857416
  • Al-Mutairi, D. K., Ghitany, M. E., & Kundu, D. (2018). Weighted Weibull distribution: Bivariate and multivariate cases. Brazilian Journal of Probability and Statistics, 32(1), 20–43. https://doi.org/10.1214/16-BJPS330
  • Alshangiti, A. M., Kayid, M., & Alarfaj, B. (2014). A new family of Marshall-Olkin extended distributions. The Journal of Computational and Applied Mathematics, 271, 369–379. https://doi.org/10.1016/j.cam.2014.04.020
  • Arshad, M., Pathak, A. K., Azhad, Q. J., & Khetan, M. (2023). Modeling bivariate data using linear exponential and Weibull distributions as marginals. Mathematica Slovaca - Journal.
  • Arshad, M., Azhad, Q. J., Gupta, N., & Pathak, A. K. (2021). Bayesian inference of unit Gompertz distribution based on dual generalized order statistics. Communications in Statistics - Simulation and Computation, 1–19. https://doi.org/10.1080/03610918.2021.1943441
  • Azhad, Q. J., Arshad, M., & Khandelwal, N. (2022). Statistical inference of reliability in multicomponent stress strength model for Pareto distribution based on upper record values. International Journal of Modelling and Simulation, 42(2), 319–334. https://doi.org/10.1080/02286203.2021.1891496
  • Bahman, T., & Mohammad, A. (2021). A new extension of Chen distribution with applications to lifetime data. Communications in Mathematics and Statistics, 9, 23–38.
  • Bai, X., Shi, Y., Ng, H. K. T., & Liu, Y. (2020). Inference of accelerated dependent competing risks model for Marshall-Olkin bivariate Weibull distribution with nonconstant parameters. The Journal of Computational and Applied Mathematics, 366, 112398–19. pp. https://doi.org/10.1016/j.cam.2019.112398
  • Balakrishnan, N., & Lai, C. D. (2009). Continuous bivariate distributions (2nd ed.). Springer.
  • Barbiero, A. (2019). A bivariate count model with discrete Weibull margins. Mathematics and Computers in Simulation, 156, 91–109. https://doi.org/10.1016/j.matcom.2018.07.003
  • Basu, A. P. (1971). Bivariate failure rate. Journal of the American Statistical Association, 66(333), 103–104. https://doi.org/10.1080/01621459.1971.10482228
  • Bebbington, M., Lai, C. D., & Zitikis, R. (2007). A flexible Weibull extension. Reliability Engineering & System Safety, 92(6), 719–726. https://doi.org/10.1016/j.ress.2006.03.004
  • Capéraà, P., & Genest, C. (1993). Spearman’s ρ is larger than Kendall’s τ for positively dependent random variables. Journal of Nonparametric Statistics, 2(2), 183–194. https://doi.org/10.1080/10485259308832551
  • Dette, H., Siburg, K. F., & Stoimenov, P. A. (2013). A copula-based non-parametric measure of regression dependence. Scandinavian Journal of Statistics, 40(1), 21–41. https://doi.org/10.1111/j.1467-9469.2011.00767.x
  • Dolati, A., Amini, M., & Mirhosseini, S. M. (2014). Dependence properties of bivariate distributions with proportional (reversed) hazards marginals. Metrika, 77(3), 333–347. https://doi.org/10.1007/s00184-013-0440-1
  • Eliashberg, J., Singpurwalla, N. D., & Wilson, S. P. (1997). Calculating the reserve for a time and usage indexed warranty. Management Science, 43(7), 966–975. https://doi.org/10.1287/mnsc.43.7.966
  • Gelman, A., Stern, H. S., Carlin, J. B., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis (3rd ed.). CRC Press.
  • Gen, Y., & Songjian, W. (2019). The gamma/Weibull customer lifetime model. Communications in Mathematics and Statistics, 7, 33–59.
  • Genest, C., & Plante, J. F. (2003). On Blest’s measure of rank correlation. Canadian Journal of Statistics, 31(1), 35–52. https://doi.org/10.2307/3315902
  • Gongsin, I. E., & Saporu, F. W. O. (2020). A bivariate conditional Weibull distribution with application. Afrika Matematika, 31(3-4), 565–583. https://doi.org/10.1007/s13370-019-00742-8
  • Gupta, R. D., & Kundu, D. (1999). Generalized exponential distributions. Australian & New Zealand Journal of Statistics, 41(2), 173–188. https://doi.org/10.1111/1467-842X.00072
  • Hanagal, D. D. (1996). A multivariate Weibull distribution. Economic Quality Control, 11, 193–200.
  • Holland, P. W., & Wang, Y. J. (1987). Dependence function for continuous bivariate densities. Communications in Statistics - Theory and Methods, 16(3), 863–876. https://doi.org/10.1080/03610928708829408
  • Jamalizadeh, A., & Kundu, D. (2013). Weighted Marshall–Olkin bivariate exponential distribution. Statistics, 47(5), 917–928. https://doi.org/10.1080/02331888.2012.670640
  • Johnson, N. L., & Kotz, S. (1975). A vector valued multivariate hazard rate. Journal of Multivariate Analysis, 5(1), 53–66. https://doi.org/10.1016/0047-259X(75)90055-X
  • Jose, K. K., Ristić, M. M., & Joseph, A. (2011). Marshall-Olkin bivariate Weibull distributions and processes. Statistical Papers, 52(4), 789–798. https://doi.org/10.1007/s00362-009-0287-8
  • Jung, M., & Bai, D. S. (2007). Analysis of field data under two-dimensional warranty. Reliability Engineering & System Safety, 92(2), 135–143. https://doi.org/10.1016/j.ress.2005.11.011
  • Kundu, D., & Gupta, R. D. (2010). A class of absolutely continuous bivariate distributions. Statistical Methodology, 7(4), 464–477. https://doi.org/10.1016/j.stamet.2010.01.004
  • Kundu, D., & Gupta, A. K. (2014). On bivariate Weibull-geometric distribution. Journal of Multivariate Analysis, 123, 19–29. https://doi.org/10.1016/j.jmva.2013.08.004
  • Lee, L. (1979). Multivariate distributions having Weibull properties. Journal of Multivariate Analysis, 9(2), 267–277. https://doi.org/10.1016/0047-259X(79)90084-8
  • Lehmann, E. L. (1966). Some concepts of dependence. The Annals of Mathematical Statistics, 37(5), 1137–1153. https://doi.org/10.1214/aoms/1177699260
  • Lu, J. C., & Bhattacharyya, G. K. (1990). Some new constructions of bivariate Weibull models. Annals of the Institute of Statistical Mathematics, 42(3), 543–559. https://doi.org/10.1007/BF00049307
  • Marshall, A. W., & Olkin, I. (1967). A generalized bivariate exponential distribution. Journal of Applied Probability, 4(2), 291–302. https://doi.org/10.2307/3212024
  • 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
  • Mirhosseini, S. M., Amini, M., Kundu, D., & Dolati, A. (2015). On a new absolutely continuous bivariate generalized exponential distribution. Statistical Methods & Applications, 24(1), 61–83. https://doi.org/10.1007/s10260-014-0276-5
  • Mudholkar, G. S., & Srivastava, D. K. (1993). Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE Transactions on Reliability, 42(2), 299–302. https://doi.org/10.1109/24.229504
  • Nandi, S., & Dewan, I. (2010). An EM algorithm for estimating the parameters of bivariate Weibull distribution under random censoring. Computational Statistics & Data Analysis, 54(6), 1559–1569. https://doi.org/10.1016/j.csda.2010.01.004
  • Nelsen, R. B. (1998). Concordance and Gini’s measure of association. Journal of Nonparametric Statistics, 9(3), 227–238. https://doi.org/10.1080/10485259808832744
  • Nelsen, R. B. (2006). An Introduction to Copulas. Second ed., Springer.
  • Park, S., & Park, J. (2018). A general class of flexible Weibull distributions. Communications in Statistics - Theory and Methods, 47(4), 767–778. https://doi.org/10.1080/03610926.2015.1118509
  • Pathak, A. K., & Vellaisamy, P. (2022). A bivariate generalized linear exponential distribution: Properties and estimation. Communications in Statistics - Simulation and Computation, 51(9), 5426–5446. https://doi.org/10.1080/03610918.2020.1771591
  • R Core Team (2020). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing.
  • Samanthi, R. G., & Sepanski, J. (2019). A bivariate extension of the beta generated distribution derived from copulas. Communications in Statistics - Theory and Methods, 48(5), 1043–1059. https://doi.org/10.1080/03610926.2018.1429626
  • Sarabia, M. J., & Emilio, G. D. (2008). Construction of multivariate distributions: A review of some recent results. SORT, 32, 3–36.
  • Shaked, M. (1977). A family of concepts of dependence for bivariate distributions. Journal of the American Statistical Association, 72(359), 642–650. https://doi.org/10.1080/01621459.1977.10480628
  • Sklar, A. (1959). Fonctions de répartition à n dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris, 8, 229–231.
  • Xie, M., Tang, Y., & Goh, T. N. (2002). A modified Weibull extension with bathtub-shaped failure rate function. Reliability Engineering & System Safety, 76(3), 279–285. https://doi.org/10.1016/S0951-8320(02)00022-4

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.