Wei, Z., Yang, F., Luo, L., and Lin, S., "The Uncertainty of Estimated Lognormal and Weibull Parameters for Test Data with Small Sample Size," SAE Technical Paper 2013-01-0945, 2013, doi:10.4271/2013-01-0945.
In this paper, the uncertainty of the estimated parameters of lognormal and Weibull distributions for test data with small sample size is investigated. The confidence intervals of the estimated parameters are determined by solving available analytical equations, and the scatters of the estimated parameters with respect to the true values are estimated by using Monte Carlo simulation approaches. Important parameters such as mean, standard deviation, and design curve are considered. The emphasis is on the interpretation and the implication of the obtained shape parameter β of the Weibull distribution function and the design curve obtained from a lognormal distribution function. Finally, the possible impact of this study on the current engineering practice is discussed.