Quel Beau Pissoir, in Art, Design, Literature and Statistics

The design of urinals for public and semi-public restrooms is difficult to standardise, as they are not intended for single users and must accommodate a wide range of anatomical and behavioural variability. Beyond technical specifications, effective design must account for   social norms related to privacy as well as hygiene and sanitation requirements. In particular, the height, shape, and dimensions of a urinal basin should minimize splashing, spillage, and dribbling beyond the rim. An adequately designed basin edge is therefore essential, and univariate or bivariate Gaussian models have traditionally been used to shape urinal design. The primary objective of this study is to examine how Gaussian distributions and heavier-tailed tanBeta distributions, such as the Cauchy distribution, which is the tangent of a Uniform random variable, can contribute to improved urinal design aimed at improving floor tidiness. We extend this approach by analysing the tangent transformations of the symmetric, Beta(1/2,1/2) and Beta(2,2) distributions. By comparing their central regions containing 68% probability, we assess their implications for basin geometry. Aside from statistical modelling, critical appraisal of statistical methodology on sampling by interviewing is considered in this multidisciplinary study, that also deals with the relevance of anatomical characteristics for the design of these indispensable urbanism commodities. Results suggest that successful urinal design requires a balance between aesthetic appeal and ergonomic effectiveness, while accounting for the substantial diversity in male anatomical and biometric characteristics, since the prevalence of some defects indicate that wider models would be more fit to ensure tidiness.