Unbiased Weibull Modulus Estimation Using Differential Cumulative Entropy

Recently, Liu (2007 Liu , J. ( 2007 ). Information Theoretic Content and Probability. Ph.D. Thesis. University of Florida, Gainesville, FL . [Google Scholar]) defined a new entropy which measures the distance between a prescribed and an empirical survival function. In this article, we use this measure called Differential Cumulative Entropy (DCE) for Weibull parameters estimation. We show that the DCE method provides biased estimations of the Weibull modulus, but utilizing unbiasing factors derived here we enhance the results. A simulation study shows the higher performance of the new method over commonly used maximum likelihood and linear regression methods in Weibull parameters estimation especially in small sample sizes.