Bayesian Survival Estimation of Pareto Distribution of the Second Kind Based on Type II Censored Data

Kim, Dal-Ho;Lee, Woo-Dong;Kang, Sang-Gil

  • 발행 : 2005.12.01


In this paper, we discuss the propriety of the various noninformative priors for the Pareto distribution. The reference prior, Jeffreys prior and ad hoc noninformative prior which is used in several literatures will be introduced and showed that which prior gives the proper posterior distribution. The reference prior and Jeffreys prior give a proper posterior distribution, but ad hoc noninformative prior which is proportional to reciprocal of the parameters does not give a proper posterior. To compute survival function, we use the well-known approximation method proposed by Lindley (1980) and Tireney and Kadane (1986). And two methods are compared by simulation. A real data example is given to illustrate our methodology.


Survival function;Noninformative prior;Lindley approximation;Tireney- Kadane approximation


  1. Arnold, B.C. and Press, S.J. (1989). Bayesian estimation and prediction for Pareto data, Journal of the American Statistical Association, Vol. 84, 1079-1084
  2. Bain, L.J. and Engelhardt, M. (1992). Introduction to Probability and Mathematical Statistics, 2nd Edition. PWS- KENT Publishing company, Boston, Massachusett
  3. Cohen, A.C. and Whitten, B.J. (1988). Parameter Estimation in Reliability and Life Span Models, Marcel Dekker, Inc. New York
  4. Davis, T.H. and Feldstein, L.M. (1979). The generalized Pareto law as a model for Progressively censored survival data, Biometrika, Vol. 66 (2), 299-306
  5. Dyer, D. (1981). Structural Probability Bounds for the Strong Pareto Law, Canadian Journal of Statistics, 9, 71-77
  6. Grimshaw, D.S. (1993). Computing Maximum Likelihood Estimates for the Generalized Pareto Distribution. Technometrics, 35, (2), 185-191
  7. Howlader, H. A and Hossain, A M. (2002). Bayesian Survival Estimation of Pareto Distribution of the Second Kind based on Failure-Censored Data, Computational Statistics & Data Analysis, 38, 301-314
  8. Kim, D. H., Lee, W. D. and Kang, S. G. (2004). Noninformative Priors for Pareto Distribution, Preprint
  9. Lindley, D.V. (1980). Approximate Bayesian Methods, in Bayesian Statistics, Bernardo, J.M., De Groot, M.H., Lindley, D.V. and smith, A.F.M., eds. Valencia, Spain: Valencia Press, 223-245
  10. Lomax, K.S. (1954). Business failures. Another example of the analysis of failure data, Journal of the American Statistical Association, Vol. 49, 847-852
  11. Santis , F.D, Mortera, J. and Nardi, A. (2001). Jeffreys priors for survival models with censored data, Journal of Statistical Planning and Inference, Vol. 99 (2), 193-209
  12. Sweeting, T.J. (2001). Coverage Probability Bias, Objective Bayes and the Likelihood Principle. Biomerika, 88, 657-675
  13. Tireney, L. and Kadane, J. (1986). Accurate approximations for posterior moments and marginals, Journal of the American Statistical Association, Vol. 81, 82-86