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Bayesian Estimation of the Survival Characteristics for a Special Case of Weighted X gamma Distribution

Jai Prakash, Vinod Kumar


In the present study, a weighted version of the xgamma distribution is introduced and its special case i.e. length biased version, isstudied as a lifetime distribution. With the help of Tierney and Kadane method of approximation, we have obtained Bayes estimators of the parameter θ, Survival function, Failure rate function and Mean time to failure under three Priors namely Gamma,Uniform and Mukherjee-Islam. The results obtained have been illustrated employing several randomly generated data sets from the proposed distribution each replicated 10000 times. The Bayes risks have been evaluated by using Squared Error Loss Function (SELF). A real-life data set has also been used to establish its utility.It is concluded that Gamma Prior is superior among the other two Priorsfor finding the Bayes estimates of the parameterθ, Survival function, Failure rate function and Mean time to failure of the length biased version of the proposed distribution.

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T.Bjerkedal; Acquisition of Resistance in Guinea Pies infected with Different Doses of Virulent Tubercle Bacilli. American Journal of Hygiene, 72(1), 130-48. (1960).

S., Das; D. Kundu;On weighted exponential distribution and its length biased version, Journal of the Indian Society for Probability and Statistics, 17(1) 57-77(2016).

R.A. Fisher; The effects of methods of ascertainment upon the estimation of frequencies, The Annals of Eugenics,6 13-25(1934).

A.K.Gupta; R.C.Tripathi; (1996).Weighted bivariate logarithmic series distributions: commun.Statist.Theory Meth. 251099-1117(1996).

X.K.Jing;Weighted Inverse weibull and Betainverseweibull distributions, Master Dissertation, Statesboro, Georgia(2017).

G. P.Patil; C. R. Rao; Weighted distributions and size-biased sampling with applications to wildlife populations and human families, Biometrics, 179-189.(1978).

G. P.Patil; J.K. Ord; On size biased sampling and related form invariant weighted distribution, The Indian Journal of Statistics,3948-61(1976).

C. R. Rao; On discrete distributions arising out of methods of a ascertainment in classical and contagious discrete distributions, G.P. Patil, ed., Pergamon Press and Statistical Publishing Society, Calcutta(1965).

C. R. Rao; Weighted distributions arising out of methods of ascertainment in a celebration of statistics, A.C. Atkinson and S.E. Fienberg, eds., Springer-Verlag, New York(1985).

N.I. Rashwan; The Double Weighted Rayleigh Distribution Properties and Estimation, International Journal of Scientific & Engineering Research 4(12) 1084-1089(2013).

N.I. Rashwan;A Length-biased version of the generalized Gamma distribution, Advances and Applications in Statistics, 32 119-137 (2013).

S.Sen; N. Chandra; S.S. Maiti; The weighted xgamma distribution: Properties and application, Journal of Reliability and Statistical Studies, 10(1)43-58(2017).

S.Sen; N. Chandra; S.S. Maiti;Survival estimation in xgamma distribution under progressively type-II right censored scheme, Model Assisted Statistics and Applications, 13(2) 107-121(2018).

X. Shi;B.O. oluyeede; M.Pararai; Theoretical Properties of weighted generalized Rayleigh and related distribution,Theoretical Mathematics and Applications, 2 45-62(2012)..

L. Tierney;J.B. Kadane; Accurate approximations for posterior moments and marginal densities. Journal of the american statistical association, 81(393), 82-86 (1986).

M. Wu; Y. Shi; Bayes estimation and expected termination time for the competing risks model from Gompertz distribution under progressively hybrid censoring with binomial removals, Journal of Computational and Applied Mathematics, 300420-431(2016).

M. Zelen;Problems in cell kinetics and the early detection of disease, in reliability and biometry, F. Proschan and R.J. Sering, eds, SIAM, Philadelphia(1974).


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