Bayes Analysis of a Three-Parameter Pareto Distribution via Sample Based Approaches

SYNOPTIC ABSTRACT This paper considers an important but less explored model, namely the three-parameter Pareto distribution that, besides having applications in many important areas, has been advocated in the context of failure time data analysis. The analysis has been done using both the Gibbs sampler vs. the Metropolis algorithm, and it has been shown that the Metropolis algorithm offers significant improvement over the Gibbs sampler. The extension of the two algorithms for censored situations is also given. For numerical illustration, we have considered both the real and the simulated data sets from the model. In the second part of the study, we illustrate the assumed model on the basis of a real data set using the tool kits of Bayesian predictive simulation ideas.

[1]  Thaung Lwin.  Estimation of the tail of the paretian law , 1972 .

[2]  Brian D. Ripley,et al.  Stochastic Simulation , 2005 .

[3]  B. Arnold,et al.  Bayesian inference for pareto populations , 1983 .

[4]  Seymour Geisser,et al.  Predicting Pareto and exponential observables , 1984 .

[5]  H. M. Aly,et al.  Estimation of the parameters of pareto distribution and the reliability function usin accelerated life testing with censoring , 1998 .

[6]  W. Michael Conklin,et al.  Monte Carlo Methods in Bayesian Computation , 2001, Technometrics.

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

[8]  Adrian F. M. Smith,et al.  Bayesian Analysis of Constrained Parameter and Truncated Data Problems , 1991 .

[9]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[10]  Xiao-Li Meng,et al.  POSTERIOR PREDICTIVE ASSESSMENT OF MODEL FITNESS VIA REALIZED DISCREPANCIES , 1996 .

[11]  Mark Carpenter,et al.  Estimating the minimum and maximum location parameters for two gamma-exponential scale mixtures , 1994 .

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

[13]  S. E. Hills,et al.  Illustration of Bayesian Inference in Normal Data Models Using Gibbs Sampling , 1990 .

[14]  Michael L. Feldstein,et al.  The generalized Pareto law as a model for progressively censored survival data , 1979 .

[15]  Danny D. Dyer,et al.  Structural probability bounds for the strong Pareto law , 1981 .

[16]  Seymour Geisser.  Interval prediction for Pareto and exponential observables , 1985 .

[17]  B. Arnold,et al.  Bayesian Estimation and Prediction for Pareto Data , 1989 .

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