Probabilistic Applications of the Schlömilch Transformation
The Schlömilch transformation, long used by mathematicians for integral evaluation, allows probability mass to be redistributed, thus transforming old distributions to new ones. The transformation is used to introduce some new families of distributions on ℛ+. Their general properties are studied, i.e., distributional shape and skewness, moments and inverse moments, hazard function, and random number generation. In general, these distributions are suitable for modeling data where the hazard function initially rises steeply. Their usefulness is illustrated by fitting some human weight data. Besides data fitting, one possible use of the new distributions could be in sensitivity or robustness studies, for example as Bayesian prior distributions.