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(This article was first published on <strong><a href="https://xianblog.wordpress.com/2016/12/12/ratio-of-uniforms-1/"> R – Xi'an's Og</a></strong>, and kindly contributed to <a rel="nofollow" href="https://www.r-bloggers.com/">R-bloggers)</a> </div>
<p><strong><a target="_blank" rel="nofollow" href="https://i2.wp.com/images-na.ssl-images-amazon.com/images/I/41knkIXE%2BoL._SX330_BO1,204,203,200_.jpg?ssl=1"><img alt="" src="https://i2.wp.com/images-na.ssl-images-amazon.com/images/I/41knkIXE%2BoL._SX330_BO1,204,203,200_.jpg?resize=222%2C333&ssl=1" data-recalc-dims="1"></a>L</strong>uca Martino pointed out to me my own and forgotten <a target="_blank" rel="nofollow" href="https://xianblog.wordpress.com/2012/05/15/generalised-ratio-of-uniforms/">review of a 2012 paper</a> of his, “<a target="_blank" rel="nofollow" href="http://arxiv.org/abs/1205.0482">On the Generalized Ratio of Uniforms as a Combination of Transformed Rejection and Extended Inverse of Density Sampling</a>” that obviously discusses a generalised version of Kinderman and Monahan’s (1977) ratio-of-uniform method. And further points out the earlier 1991 paper by Jon Wakefield, Alan Gelfand and Adrian Smith that contains the general form I rediscovered <a target="_blank" rel="nofollow" href="https://xianblog.wordpress.com/2016/11/04/ratio-of-uniforms-3/">a few posts ago</a>… Called the GRoU in <a target="_blank" rel="nofollow" href="http://arxiv.org/abs/1205.0482">Martino et al.</a>. While the generalisation in the massive <a target="_blank" rel="nofollow" href="http://arxiv.org/abs/1205.0482">arXiv document</a> is in finding Φ such that the above region is bounded and can be explored by uniform sampling over a box.</p>
<p>Neither reference mentions using the cdf transform, though, which does guarantee a bounded ratio-of-uniform set in u. (An apparent contradiction with <a target="_blank" rel="nofollow" href="http://arxiv.org/abs/1205.0482">Martino et al.</a>  statement (34), unless I am confused. Maybe due to using Φ⁻¹ instead of Φ?) But I still wonder at the usefulness of my derivations those past weeks!</p>
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