The evaluation of evidence for exponentially distributed data

At present, likelihood ratios for two-level models are determined with the use of a normal kernel estimation procedure when the between-group distribution is thought to be non-normal. An extension is described for a two-level model in which the between-group distribution is very positively skewed and an exponential distribution may be thought to represent a good model. The theoretical likelihood ratio is derived. A likelihood ratio based on a biweight kernel with an adaptation at the boundary is developed. The performance of this kernel is compared alongside those of normal kernels and normal and exponential parametric models. A comparison of performance is made for simulated data where results may be compared with those of theory, using the theoretical model, as the true ∗School of Mathematics, King’s Buildings, The University of Edinburgh, Mayfield Road, Edinburgh, EH9 3JZ; e-mail: [email protected]; tel: +44(0) 131 650 4877; fax: +44(0) 131 650 6553.