Estimation of Weibull parameters from common percentiles

Abstract

Estimation of Weibull distribution shape and scale parameters is accomplished through use of symmetrically located percentiles from a sample. The process requires algebraic solution of two equations derived from the cumulative distribution function. Three alternatives examined are compared for precision and variability with maximum likelihood (MLE) and least squares (LS) estimators. The best percentile estimator (using the 10th and 90th) is inferior to MLE in variability and to one least squares estimator in accuracy and variability to a small degree. However, application of a correction factor related to sample size improves the percentile estimator substantially, making it more accurate than LS.

Keywords:

• Parameter estimation
• Weibull distribution
• percentiles