Resumen de The normal distribution in some constrained sample spaces

Glòria Mateu Figueras , Vera Pawlowsky Glahn , Juan José Egozcue Rubí

• Phenomena with a constrained sample space appear frequentl y in practice. This is the case, for example, with strictly positive data, or with compositi onal data, such as percentages or proportions. If the natural measure of difference is not the absolute one, simple algebraic properties show that it is more convenient to work with a geom etry different from the usual Euclidean geometry in real space, and with a measure differe nt from the usual Lebesgue measure, leading to alternative models that better fit the ph enomenon under study. The general approach is presented and illustrated using the normal dist ribution, both on the positive real line and on the D -part simplex. The original ideas of McAlister in his introd uction to the lognormal distribution in 1879, are recovered and updated.