Applications of Burr III-Weibull quantile function in reliability analysis

References

• Burr, I. W. (1942). Cumulative frequency functions. The Annals of Mathematical Statistics, 13(2), 215–232. https://doi.org/10.1214/aoms/1177731607
   Google Scholar
• Dagum, C. (2008). A new model of personal income distribution: specification and estimation (pp. 3–25). Springer. https://doi.org/10.1007/978-0-387-72796-7_1
   Google Scholar
• Gilchrist, W. (2000). Statistical modelling with quantile functions. Chapman and Hall/CRC.
   Google Scholar
• Govindarajula, Z. (1977). A class of distributions useful in life testing and reliability. IEEE Transactions on Reliability, 26(1), 67–69. https://doi.org/10.1109/TR.1977.5215079
   Web of Science ®Google Scholar
• Hallinan Jr, A. J. (1993). A review of the Weibull distribution. Journal of Quality Technology, 25(2), 85–93. https://doi.org/10.1080/00224065.1993.11979431
   Web of Science ®Google Scholar
• Hankin, R. K., & Lee, A. (2006). A new family of non-negative distributions. Australian & New Zealand Journal of Statistics, 48(1), 67–78. https://doi.org/10.1111/anzs.2006.48.issue-1
   Web of Science ®Google Scholar
• Hastings Jr, C., Mosteller, F., Tukey, J. W., & Winsor, C. P. (1947). Low moments for small samples: A comparative study of order statistics. The Annals of Mathematical Statistics, 18(3), 413–426. https://doi.org/10.1214/aoms/1177730388
   Google Scholar
• Hosking, J. R. (1990). L-moments: Analysis and estimation of distributions using linear combinations of order statistics. Journal of the Royal Statistical Society: Series B (Methodological), 52(1), 105–124. http://www.jstor.org/stable/2345653
   Web of Science ®Google Scholar
• Huang, S., & B. O. Oluyede (2014). Exponentiated Kumaraswamy-Dagum distribution with applications to income and lifetime data. Journal of Statistical Distributions and Applications, 1(1), 1–20. https://doi.org/10.1186/2195-5832-1-8
   Google Scholar
• Lai, C. D., & Xie, M. (2006). Stochastic ageing and dependence for reliability. Springer Science & Business Media.
   Google Scholar
• Lai, C. D., Xie, M., & Murthy, D. N. P. (2003). A modified Weibull distribution. IEEE Transactions on Reliability, 52(1), 33–37. https://doi.org/10.1109/TR.2002.805788
   Web of Science ®Google Scholar
• Mielke, P. W. (1973). Another family of distributions for describing and analyzing precipitation data. Journal of Applied Meteorology and Climatology, 12(2), 275–280. https://doi.org/10.1175/1520-0450(1973)012<0275:AFODFD>2.0.CO;2
   Google Scholar
• Mudholkar, G. S., & Kollia, G. D. (1994). Generalized Weibull family: A structural analysis. Communications in Statistics-Theory and Methods, 23(4), 1149–1171. https://doi.org/10.1080/03610929408831309
   Web of Science ®Google Scholar
• Nadarajah, S., & Kotz, S. (2008). Strength modeling using Weibull distributions. Journal of Mechanical Science and Technology, 22(7), 1247–1254. https://doi.org/10.1007/s12206-008-0426-5
   Web of Science ®Google Scholar
• Nair, N. U., & Sankaran, P. G. (2009). Quantile-based reliability analysis. Communications in Statistics-Theory and Methods, 38(2), 222–232. https://doi.org/10.1080/03610920802187430
   Web of Science ®Google Scholar
• Nair, N. U., Sankaran, P. G., & Balakrishnan, N. (2013). Quantile-based reliability analysis. Springer Science & Business Media.
   Google Scholar
• Nair, N. U., Sankaran, P. G., & Kumar, B. V. (2008). Total time on test transforms of order n and their implications in reliability analysis. Journal of Applied Probability, 45(4), 1126–1139. https://doi.org/10.1239/jap/1231340238
   Web of Science ®Google Scholar
• Parzen, E. (1979). Nonparametric statistical data modeling. Journal of the American Statistical Association, 74(365), 105–121. https://doi.org/10.1080/01621459.1979.10481621
   Web of Science ®Google Scholar
• Ramberg, J. S., & Schmeiser, B. W. (1972). An approximate method for generating symmetric random variables. Communications of the ACM, 15(11), 987–990. https://doi.org/10.1145/355606.361888
   Web of Science ®Google Scholar
• Sankaran, P. G., & Dileep Kumar, M. (2018). A new class of quantile functions useful in reliability analysis. Journal of Statistical Theory and Practice, 12(3), 615–634. https://doi.org/10.1080/15598608.2018.1448732
   Web of Science ®Google Scholar
• Sankaran, P. G., Nair, N. U., & Midhu, N. N. (2016). A new quantile function with applications to reliability analysis. Communications in Statistics-Simulation and Computation, 45(2), 566–582. https://doi.org/10.1080/03610918.2013.867992
   Web of Science ®Google Scholar
• Sankaran, P. G., & Unnikrishnan Nair, N. (2009). Nonparametric estimation of hazard quantile function. Journal of Nonparametric Statistics, 21(6), 757–767. https://doi.org/10.1080/10485250902919046
   Web of Science ®Google Scholar
• Sreelakshmi, N., Kattumannil, S. K., & Asha, G. (2018). Quantile based tests for exponentiality against DMRQ and NBUE alternatives. Journal of the Korean Statistical Society, 47(2), 185–200. https://doi.org/10.1016/j.jkss.2017.12.003
   Web of Science ®Google Scholar