International Journal of Statistics and Applications
pISSN: 21685193 eISSN: 21685215
2018; 8(5): 274290
doi:10.5923/j.statistics.20180805.06
Mohammed H. AbuJarad, Athar Ali Khan
Department of Statistics and Operations Research, AMU, Aligarh, India
Correspondence to: Mohammed H. AbuJarad, Department of Statistics and Operations Research, AMU, Aligarh, India.
Email: 
Copyright © 2018 The Author(s). Published by Scientific & Academic Publishing.
This work is licensed under the Creative Commons Attribution International License (CC BY).
http://creativecommons.org/licenses/by/4.0/
In this article, the discussion has been carried out on the generalization of three distribution by means of exponential, exponentiated exponential and exponentiated extension. We set up three and four parameters life model called the ToppLeone exponential distribution, ToppLeone exponentiated exponential distribution and ToppLeone exponentiated extension distribution. We give extensive consequence of the, survival function and hazard rate function. To fit this model as survival model and hazard rate function we adopted to use Bayesian approach. A real survival data set is used to illustrate. application is done by R and Stan and suitable illustrations are prepared. R and Stan codes have been given to actualize censoring mechanism via optimization and also simulation tools.
Keywords: ToppLeone exponential, ToppLeone exponentiated exponential, ToppLeone exponentiated extension, Posterior, Simulation, RStan, Bayesian Inference, R, HMC
Cite this paper: Mohammed H. AbuJarad, Athar Ali Khan, Bayesian Survival Analysis of ToppLeone Generalized Family with Stan, International Journal of Statistics and Applications, Vol. 8 No. 5, 2018, pp. 274290. doi: 10.5923/j.statistics.20180805.06.
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Figure 1. Probability density plots, cdf, survival and hazard curves of ToppLeone Exponential distribution for different value 
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Figure 2. Probability density plots, cdf, survival and hazard curves of ToppLeone Exponential distribution for different value 
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Figure 3. Probability density plots, cdf, survival and hazard curves of ToppLeone Exponential distribution for different value 
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Figure 4 
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Figure 5. Caterpillar plot for ToppLeone Exponential model 
Figure 6. Checking model convergence using rstan, through inspection of the traceplots or the autocorrelation plot 
Figure 7. Checking model convergence using coda, through inspection of the simulated posterior density plots with trace plots of regressor variables obtained by HMC 

Figure 8. Caterpillar plot for ToppLeone Exponentiated Exponential model 
Figure 9. Checking model convergence using rstan, through inspection of the traceplots or the autocorrelation plot 
Figure 10. Checking model convergence using coda, through inspection of the simulated posterior density plots with trace plots of regressor variables obtained by HMC 

Figure 11. Caterpillar plot for ToppLeone Exponential Extension model 
Figure 12. Checking model convergence using rstan, through inspection of the traceplots or the autocorrelation plot 
Figure 13. Checking model convergence using coda, through inspection of the simulated posterior density plots with trace plots of regressor variables obtained by HMC 

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