Full posterior analysis of three parameter lognormal distribution using gibbs sampler

The paper provides full posterior analysis of three parameter lognormal distribution using Gibbs Sampler, an important and useful Markov chain Monte Carlo technique in Bayesian computation. The extension of the algorithm is given to cover the case of censored data. It has been found that the censoring which creates special problem in the analysis of lognormal model with non-closed form cdf, can be routinely tackled by the use of Gibbs sampler. Suitable numerical illustrations are provided for both complete and censored situations.

[1]  Richard L. Smith,et al.  A Comparison of Maximum Likelihood and Bayesian Estimators for the Three‐Parameter Weibull Distribution , 1987 .

[2]  Bruce M. Hill,et al.  The Three-Parameter Lognormal Distribution and Bayesian Analysis of a Point-Source Epidemic , 1963 .

[3]  Further considerations of modified moment estimators for weibull and lognormal parameters , 1996 .

[4]  The Recent Depression in Agriculture as Shown in the Accounts of an Oxford College, 1876-90 , 1892 .

[5]  Jerald F. Lawless,et al.  Statistical Models and Methods for Lifetime Data. , 1983 .

[6]  J. Aitchison,et al.  The Lognormal Distribution. , 1958 .

[7]  P. R. Fisk,et al.  Distributions in Statistics: Continuous Multivariate Distributions , 1971 .

[8]  R. Wixley,et al.  Estimators Based on Order Statistics of Small Samples from a Three-Parameter Lognormal Distribution , 1970 .

[9]  G. C. Tiao,et al.  Bayesian inference in statistical analysis , 1973 .

[10]  J. Lawless.  Statistical Models and Methods for Lifetime Data , 2002 .

[11]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[12]  A. H. Moore,et al.  Local-Maximum-Likelihood Estimation of the Parameters of Three-Parameter Lognormal Populations from Complete and Censored Samples , 1966 .

[13]  L. Devroye.  Non-Uniform Random Variate Generation , 1986 .

[14]  W. Gilks,et al.  Adaptive Rejection Sampling for Gibbs Sampling , 1992 .

[15]  H. Martz.  Bayesian reliability analysis , 1982 .

[16]  Adrian F. M. Smith,et al.  Bayesian computation via the gibbs sampler and related markov chain monte carlo methods (with discus , 1993 .

[17]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.