The Use of a Log-Normal Prior for the Student t-Distribution

It is typically difficult to estimate the number of degrees freedom due leptokurtic nature Student t-distribution. Particularly in studies with small sample sizes, special care needed concerning prior choice order ensure that analysis not overly dominated by any distribution. In this article, popular priors used existing literature are examined characterizing their distributional properties on an effective support where it desirable concentrate most probability mass. Additionally, we suggest a log-normal as viable option. We show Bayesian estimator based compares favorably other estimators previously proposed via simulation and financial applications.