Bayesian inference for exponentiated  Pareto model with application to bladder cancer remission time

Sanjay Kumar  Singh; Umesh  Singh; Manoj  Kumar

doi:https://doi.org/10.59170/stattrans-2014-027

Bayesian inference for exponentiated Pareto model with application to bladder cancer remission time

Sanjay Kumar Singh Department of Statistics, Banaras Hindu University,Varanasi-221005 , Umesh Singh Department of Statistics and DST-CIMS, Banaras Hindu University,Varanasi-221005 , Manoj Kumar Assistant Prof. (Statistics), Department of School of Basic Science and Research, Sharda University, Greater Noida, UP. Statistics in Transition new series, vol. 15, 2014, 3, pages: 403-426 Published online: 1 September 2014 https://doi.org/10.59170/stattrans-2014-027

128 Views 11 Downloads

ARTICLE

(English) PDF

ABSTRACT

Maximum likelihood and Bayes estimators of the unknown parameters and the expected experiment times of the exponentiated Pareto model have been obtained for progressive type-II censored data with binomial removal scheme. Markov Chain Monte Carlo (MCMC) method is used to compute the Bayes estimates of the parameters of interest. The generalized entropy loss function and squared error loss function have been considered for obtaining the Bayes estimators. Comparisons are made between Bayesian and maximum likelihood (ML) estimators via Monte Carlo simulation. The proposed methodology is illustrated through real data

KEYWORDS

PT-II CBR, MLE, bayes estimators, average experiment time

REFERENCES

AARSET, M. W., (1985). The null distribution for a test of constant versus bathtub failure rate. Scandinavian Journal of Statistics, 12(1):55-68.

AFIFY, W. M., (2010). On estimation of the exponentiated Pareto distribution under different sample scheme. Applied Mathematical Sciences, 4(8):393–402.

ARNOLD, B. C., PRESS, S. J., (1983). Bayesian inference for Pareto populations.J.Econom., 21:287-306.

BALAKRISHNAN, N., (2007). Progressive methodology: An appraisal (with dis cussion). Test, 16 (2):211–259.

BALAKRISHNAN, N., AGGARWALLA, R., (2000). Progressive Censoring: The ory, Methods and Applications. Birkhauser, Boston.

BALAKRISHNAN, N., KANNAN, N., (2001). Point and Interval Estimation for Parameters of the Logistic Distribution Based on Progressively Type-II Censored Samples, in Handbook of Statisticsm N. Balakrishnan and C. R. Rao, 20. Eds.Amsterdam, North-Holand.

CALABRIA, R., PULCINI, G., (1996). Point estimation under-asymmetric loss functions for life-truncated exponential samples. Commun. statist. Theory meth.,25(3):585–600.

CHILDS, A., BALAKRISHNAN, N., (2000). Conditional inference procedures for the Laplace distribution when the observed samples are Progressively censored.Metrika, 52:253–265.

COHEN, A. C., (1963). Progressively censored samples in life testing. Technomet rics, pages 327–339.

EISSA, F. H., NASSAR, M. M.,(2004). Bayesian estimation for the exponentiated Weibull model. Communication in Statistics Theory and Methods, 33:2343–2236.

GUPTA, R. C., GUPTA, R. D., GUPTA, P. L., (1998). Modeling failure time data by Lehman alternatives. Commun. Statist. - Theory Meth., 27(4):887–904.

GUPTA, A., UPADHYAY, S. K., (2010). A Bayes analysis of modified Weibull distribution via Markov chain monte carlo simulation. Journal of Statistical Com putation and Simulation, 80(3):241–254.

JAIN, M. K., IYENGAR, S. R. K., JAIN, R. K.,(1984). Numerical Methods for Scientific and Engineering Computation. New Age International (P) Limited, Pub lishers, New Delhi, fifth edition.

JOHANSON, N. L., KOTZ, S., BALAKRISHNAN, N., (1994). Continuous Uni variate Distributions, volume 1. Wiley, New York, 2 edition.

JUNG, J., CHUNG, Y., KIM, C.,(2011). Bayesian estimation for the exponentiated Weibull model under type II progressive censoring. Statistical Papers (accepted).

LEE, E. T., WANG, J. W.,(2003). Statistical Methods for Survival Data Analysis.Wiley, New York, 3rd edition.

LUZ, M. ZEA, SILVA RODRIGO, B., BOURGUIGNON, M., ANDREA, S., GAUSS COREIRO, M., (2012). The Beta Exponentiated Pareto Distribution with Applica tion to Bladder Cancer Susceptibility. International Journal of Statistics and Prob ability, 1(2):8–19.

MOUSA, M., JAHEEN, Z., (2002). Statistical inference for the burr model based on progressively censored data. An International Computers and Mathematics with Applications,, 43:1441–1449.

NG, K., CHAN, P. S.,BALAKRISHAN, N.,(2002). Estimation of parameters from progressively censored data using an algorithm. Computational Statistics and Data Analysis, 39:371–386.

SHAWKY, A. I., HANNA, H. ABU-ZINADAH.,(2009). Exponentiated Pareto dis tribution: Different method of estimations. Int. J.Contemp. Math. Sciences, 4(14):677–693.

VASISHTA, N., SMITH, A. F. M., UPADHYAY, S. K., (2001). Bayes inference in life testing and reliability via Markov chain Monte Carlo simulation. Sankhya, A 63(1):15–20.

WU, S. J., CHANG, C. T. (2002). Parameter estimations based on exponential pro gressive type II censored with binomial removals. International Journal of Informa tion and Management Sciences, 13:37–46.

WU, S. J., CHANG, C. T., (2003). Inference in the Pareto distribution based on progressive type II censoring with random removales. Journal of Applied Statistics,30:163–172.

YANG, C., TSE, S. K., YUEN, H. K., (2000). Statistical analysis of Weibull dis tributed life time data under type II progressive censoring with binomial removals.Jounal of Applied Statistics, 27:1033–1043.

YUEN, H. K., TSE, S. K., (1996). Parameters estimation for Weibull distribution under progressive censoring with random removal. Journal Statis. Comput. Simul,55:57–71