Least-squares and minimum chi-square estimation in a discrete Weibull model

References

• Barbiero, A. (2016). A comparison of methods for estimating parameters of the type I discrete Weibull distribution. Statistics and its Interface 9(2):203–212.
   Google Scholar
• Barbiero, A. (2015). Discrete Weibull: Discrete Weibull distribution. R PackageVersion 1.0.1. Available at: https://CRAN.R-project.org/package=DiscreteWeibull
   Google Scholar
• Berkson, J. (1980). Minimum chi-square, not maximum likelihood!. The Annals of Statistics 8(3):457–487.
   Google Scholar
• Crowe, D., Feinberg, A. (2001). Design for Reliability. Boca Raton, FL: CRC Press.
   Google Scholar
• Cullen, M. J., Walsh, J., Nicholson, L. V., Harris, J. B. (1990). Ultrastructural localization of dystrophin in human muscle by using gold immunolabelling. Proceedings of the Royal Society of London. Series B 20:197–210.
   Google Scholar
• Efron, B. (1982). The Jackknife, the Bootstrap, andOther Resampling Plans. Philadelphia, PA:Society for industrial and applied mathematics.
   Google Scholar
• Englehardt, J. D., Li, R. (2011). The discrete Weibull distribution: An alternative for correlated counts with confirmation for microbial countsin water. Risk Analysis 31(3):370–381.
   Google Scholar
• Ghitany, M. E., Al-Mutairi, D. K., Nadarajah, S. (2008). Zero-truncated Poisson–Lindley distribution and its application. Mathematics and Computers in Simulation 79(3):279–287.
   Google Scholar
• Harris, R. R., Kanji, G. K. (1983). On the use of minimum chi-square estimation. Journal of the Royal Statistical Society. Series D 32(4):379–394.
   Google Scholar
• Kedem, B., Wu, Y. (1997). Minimum Chi-square vs Least Squares in Grouped Data. Technical Report, Mathematics Department and Institute for System Research, University of Marylan, USA, pp. 97–37.
   Google Scholar
• Khan, M. S. A., Khalique, A., Abouammoh, A. M. (1989). On estimating parameters in a discrete Weibull distribution. IEEE Transactions on Reliability 38(3):348–350.
   Google Scholar
• Kulasekera, K. B. (1993). Approximate MLE’s of the parameters of a discrete Weibull distribution with type I censored data. Microelectronics Reliability 34(7):1185–1188.
   Google Scholar
• Nakagawa, T., Osaki, S. (1975). The discrete Weibull distribution. IEEE Transactions on Reliability 24(5):300–301.
   Google Scholar
• Neyman, J. (1949). Contribution to the theory of the χ2 test. In: Proceedings of the First Berkeley Symposium in Mathematics and Statistics, Berkeley, CA: University of California Press, pp. 239–273.
   Google Scholar
• Osaki, S. (1985). Stochastic System Reliability Modelling. Singapore: World Scientific.
   Google Scholar
• Padgett, W. J., Spurrier, J. D. (1985). Discrete failure models. IEEE Transactions on Reliability 34(3):253–256.
   Google Scholar
• Pearson, K. (1900). On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. Philosophical Magazine 50(302):157–175.
   Google Scholar
• R Development Core Team, (2015). R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. Available at: http://www.R-project.org/.
   Google Scholar
• Sen, P. K., Singer, J. M. (1994). Large Sample Methods in Statistics: An Introduction with Applications. New York: Chapman & Hall/CRC.
   Google Scholar
• Stein, W. E., Dattero, R. (1984). A new discrete Weibull distribution. IEEE Transactions on Reliability 33(2):196–197.
   Google Scholar
• Wang, F. K. (2000). A new model with bathtub-shaped failure rate using an additive Burr XII distribution. Reliability Engineering and System Safety 70(3):305–312.
   Google Scholar
• Wu, J.-W., Hung, W.-L., Tsai, C.-H. (2004). Estimation of parameters of the Gompertz distribution using the least squares method. Applied Mathematics and Computation 158(1):133–147.
   Google Scholar