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.     

How do we capture 15 years of complex and meaningful data about young people's lives?

Abstract

This paper describes the development of a method of data collection, which captures the complexity of living situations, family dynamics and key life events of teenagers. This ‘Life History Calendar’ was adapted from earlier life history calendar methods for a multidisciplinary intergenerational study. The new calendar is able to record details of 15 years of teenage participants’ lives and can be administered to teenagers and their parents to show changes over individual lives and difference between individuals in a cohort. Referring to some preliminary data, we show that the calendar is a practical and effective method of data collection, which will be useful to researchers and practitioners working with young people and their families.