Sankhya: The Indian Journal of Statistics

2001, Volume 63, Series B, Pt. 1, pp. 3--9

LIKELIHOOD AND POSTERIOR SHAPES IN JOHNSON'S S SUB B SYSTEM

By

EFTHYMIOS G. TSIONAS Athens University of Economics and Business, Athens, Greece

SUMMARY. The paper develops Bayesian analysis in the context of samples from Johnson's $S_B$ system of distributions. It is shown that the likelihood may have extremely fat tails, which is responsible for the absurd values that parameters often assume in maximum likelihood estimation, as reported in the literature. Next, Jeffrey's non-informative prior for the problem is derived and it is shown that resulting posterior inferences are well behaved. The method is illustrated with artificial data, as well as an application to stock returns associated with the Dow-Jones index. The sampling performance of a posterior mode estimator is examined in a Monte Carlo experiment.

AMS (1991) subject classification. 61C10, 62F15.

Key words and phrases. Bayesian analysis, lognormal distribution, systems of distributions, posterior mode estimator.

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