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