Using the mean deviation in the elicitation of the prior distribution

The mean deviation about an arbitrary point a of a probability distribution, [delta]a(X) = E(vb;X - avb;), is a measure of dispersion seldom encountered in statistical applications. However, when this point is taken to be the mean or the median, the mean deviation has a meaningful interpretation and can be useful in soliciting and quantifying subjective information for Bayesian analysis. In this article we present the basic properties of the mean deviation and focus on its use in determining the prior distribution. Only results related to the Beta family are presented here, but results for other common distributions are also available.