Estimation of the Weibull parameters by Kullback-Leibler divergence of Survival functions

Recently, a new entropy based divergence measure has been introduced which is much like Kullback-Leibler divergence. This entropy measures the distance between an empirical and a prescribed survival function and is a lot easier to compute in continuous distributions than the K-L divergence. In this paper we show that this distance converges to zero with increasing sample size and we apply it to estimate Weibull parameters. Detailed simulations show a higher performance of the new estimation method than the commonly used maximum likelihood and linear regression methods in Weibull scale parameter estimation. Using unbiasing factors provided in this paper for Weibull shape parameter estimation, one can obtain unbiased estimation for Weibull modulus.