An Application of Generalized EntropyOptimization Methods in Survival Data Analysis

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Shamilov A., Kalathilparmbil Ç., Özdemir S.

Journal of Modern Physics, vol.2017, no.8, pp.349-364, 2017 (Peer-Reviewed Journal)

  • Publication Type: Article / Article
  • Volume: 2017 Issue: 8
  • Publication Date: 2017
  • Doi Number: 10.4236/jmp.2017.83024
  • Journal Name: Journal of Modern Physics
  • Journal Indexes: Other Indexes
  • Page Numbers: pp.349-364
  • Van Yüzüncü Yıl University Affiliated: Yes


In this paper, survival data analysis is realized by applying Generalized Entropy Optimization Methods (GEOM). It is known that all statistical distributions can be obtained as MaxEnt distribution by choosing corresponding moment functions. However, Generalized Entropy Optimization Distributions (GEOD) in the form of MinMaxEnt,MaxMaxEnt distributions which are obtained on basis of Shannon measure and supplementary optimization with respect to characterizing moment functions, more exactly represent the given statistical data. For this reason, survival data analysis by GEOD acquires a new significance. In this research, the data of the life table for engine failure data (1980) is examined. The performances of GEOD are established by Chi-Square criteria, Root Mean Square Error (RMSE) criteria and Shannon entropy measure, Kullback-Leibler measure. Comparison of GEOD with each other in the different senses shows that along of these distributions ( ) MinMaxEnt 4 is better in the senses of Shannon measure and of KullbackLeibler measure. It is showed that, ( ) (( ) ) MinMaxEnt MaxMaxEnt 3 4 is more suitable for statistical data among (MinMaxEnt , 1, 2,3, 4 MaxMaxEnt , 1, 2,3, 4 ) (( ) ) m m m m = = . Moreover, ( ) MinMaxEnt 3 is better for statistical data than ( ) MaxMaxEnt 4 in the sense of RMSE criteria. According to obtained distribution ( ) MinMaxEnt 3 (( ) ) MaxMaxEnt 4 estimator of Probability Density Function ( ) ˆ f t , Cumulative Distribution Function ( ) F t ˆ , Survival Function ( ) ˆ S t and Hazard Rate ( ) ˆ h t are evaluated and graphically illustrated. The results are acquired by using statistical software MATLAB