Inference on Ratio of two Medians

The problem of interest is confidence interval for ratio of two location parameters. The classical Fieller's theorem yields such a confidence interval for ratio of normal means. Resulting CI may sometimes be inadmissible. Also a median may be more appropriate location parameter if the parent distribution is skew. We explore the sampling distribution of ratio of two medians as an alternative to Fieller's theorem. Probability density function has been obtained for this statistic in case of Weibull parent populations. Use of this result to obtain confidence intervals becomes intractable for moderate sample sizes. A simulation based approach is therefore proposed. Results are applied to a study of two skin care products, based on dermatological assessment. Lastly we also explore the possibility of using the ‘proportional hazards’ approach for this purpose.