Generalized Kaplan Meier Estimator for Fuzzy Survival Times

• Authors: Shafiq Muhammad , Viertl Reinhard

Title variants

PL

Uogólniony estymator Kaplana Meiera dla rozmytego czasu przeżycia

• Languages of publication: PL EN

Abstracts

EN

Survival analysis can be defined as a set of methods where the response of interest is the time until a specified event occurred. The most common specified event is death and the related time is called survival time or life time in medical sciences. The Kaplan Meier estimator is one of the popular methods for precise survival times. It is natural that life time is of a continuous nature, therefore it is unrealistic to treat life time observations as precise numbers. In [Viertl 2009] it is shown that life time observations are not precise numbers, but more or less fuzzy. In this study a Generalized Kaplan Meier estimator for fuzzy survival time observations is proposed.

Keywords

characterizing function; fuzzy numbers; Kaplan Meier estimator; non-precise data; survival time

• Publisher: Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
• Journal: Śląski Przegląd Statystyczny
• Year: 2015
• Issue: 13 (19)

Contributors

author

Shafiq Muhammad

author

Viertl Reinhard

References

• Deshpande J.V., Purhit S.G., Life Time Data: Statistical Models and Methods, World Scientific Publishing, Singapore 2005.
• Huang H.-Z., Zuo M.J., Sun, Z.-Q., Bayesian reliability analysis for fuzzy lifetime data, “Fuzzy Sets and Systems” 2006, Vol. 157(12), pp. 1674–1686.
• Kaplan E.L., Meier P., Nonparametric estimation from incomplete observations, “Journal of the American Statistical Association” 1958, Vol. 53(282), pp. 457–481.
• Klir G., Yuan B., Fuzzy Sets and Fuzzy Logic – Theory and Applications, Upper Saddle River: Prentice Hall, 1995.
• Lee E.T., Wang J.W, Statistical Methods for Survival Data Analysis, Wiley, New Yersey 2003.
• Lee K.H., First Course on Fuzzy Theory and Applications, Springer, Heidelberg 2005.
• Viertl R., On reliability estimation based on fuzzy lifetime data, “Journal of Statistical Planning and Inference” 2009, Vol. 139(5), pp. 1750–1755.
• Viertl R., Statistical Methods for Fuzzy Data, Wiley, Chichester 2011.
• Viertl R., Hareter D., Beschreibung und Analyse unscharfer Information – Statistische Methoden für unscharfe Daten, Springer, Wien 2006.
• Wu H.-C., Statistical confidence intervals for fuzzy data, “Expert Systems with Applications” 2009, Vol. 36(2), pp. 2670–2676.