BAYESIAN ESTIMATION OF RELIABILITY IN TWO- PARAMETER GEOMETRIC DISTRIBUTION
Keywords:
ML Estimator, Quasi-Bayes Estimate, Unbiased EstimatorAbstract
Bayesian estimation of reliability of a component, R(t) = P(X ≥ t) , when X follows two-parameter geometric distribution, has been considered. Maximum Likelihood Estimator (MLE), an Unbiased Estimator and Bayesian Estimator have been compared. Bayesian estimation of component reliability R = P ( X ≤ Y ) , arising under stress-strength setup, when Y is assumed to follow independent two-parameter geometric distribution has also been discussed assuming independent priors for parameters under different loss functions.
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References
Barlow, R.E. and Proschan, F. (1967). Mathematical Theory of Reliability, John Willy &
Sons, Inc., New York.
Bhattacharya, S.K. and Kumar, S. (1985). Discrete life testing, IAPQR Transactions, 13,
p. 71-76.
Krishna, H. and Jain, N. (2002). Classical and Bayes Estimation of Reliability
Characteristics of some Basic System Configurations with Geometric Lifetimes of
Components, IAPQR Transactions, 27, p. 35-49.
Maiti, S.S. (1995). Estimation of ( )YXP ≤ in the geometric case, Journal of the
Indian Statistical Association, 33, p. 87-91.
Maiti, S.S. (2005). Bayesian Estimation of ( )YXP ≤ for some Discrete Life
Distributions, Contributions to Applied and Mathematical Statistical, 3, p. 81-96.
Maiti, S.S. (2006). On Estimation of ( )YXP ≤ for Discrete Distributions useful in
Life Testing, IAPQR Transactions, 31, p. 39-46.
Maiti, S.S. and Kanji, A. (2005). A note on Characterization of ( )YXP ≤ for Discrete
Life Distributions, Journal of Applied Statistical Science, 14, p. 275-279.
Maiti, S.S., Murmu, S. and Chattopadhyay, G. (2015). Inference on Reliability for Two-
parameter Geometric Distribution, International Journal of Agricultural and
Statistical Sciences, 11(2) (to appear).
Sathe, Y.S. and Dixit, U.J. (2001). Estimation of ( )YXP ≤ in the negative binomial
distribution, Journal of Statistical Planning and Inference, 93, p. 83-92.
Sinha, S.K. (1986). Reliability and Life Testing, Wiley Eastern Limited, New Delhi.
Yakub, M. and Khan, A.H. (1981). Geometric failure law in life testing, Pure and
Applied Mathematika Science, 14, p. 69-76.
