Bayesian Estimation of the Hybridisation Parameter for the Normal-Log-Normal Case

The log-normal (LN) distribution is the most frequently used statistical model for occupational radiation data. This distribution was fitted to, for example, the external annual radiation doses of diagnostic X ray workers in Germany, of fuel reprocessing and fabrication workers in the US, and of a variety of industrial radiation workers in Canada. In 1981 a seminal paper was published which questioned the widespread and often uncritical use of the lognormal (LN) model and proposed a new distribution called the hybrid-log-normal (HLN) distribution. A random quantity (e.g. annual external dose) X is HLN is Y = ?X + In?X ~ N(µ,s2). By comparison X is LN is Y = InX "N(µ,s2). Previously a graphical procedure has been given and regression analysis for the estimation of the parameters of an HLN distribution has been mentioned. We present a Bayesian procedure for the estimation of the hybridisation parameter p for a specific prior distribution for ?,µ and s. Figures illustrate the influence of two observations on the prior via the likelihood.