5. Acknowledgements

We are indebted to James W. Vaupel, Francesco Billari, Tan Qihua, Heiner Maier, the members of the Laboratory of Survival and Longevity at the Max Planck Institute for Demographic Research and two anonymous referees for many helpful comments and suggestion that have greatly improved this paper. We gratefully acknowledge the support received for this research by the Max Planck Institute for Demographic Research and the National Statistical Institute (NSI) in Bulgaria. The Bulgarian mortality data has been made available by the National Statistical Institute of Bulgaria, and we are greatly indebted to Ekaterina Arnaudova, Ivan Balev and Mariana Dimova for their help and support in establishing this database.