Nonnegative random variables arise in many contexts, as magnitudes of physical objects, as wind speeds, material strengths, life lengths, as well as in economic data. Whereas the normal distribution plays a central role for random variables that take on both positive and negative values, it is not generally a good model for nonnegative data. However, for nonnegative data, there is no distribution as basic as the normal distribution, with its foundation in the central limit theorem. Indeed, there are a number of competitors that serve as models for nonnegative data.
Distributions are classified as nonparametric, semiparametric and parametric families. In the nonparametric category there are no assumptions about the underlying distributions, but there may be qualitatively conditioned characteristics. For example, that the density is unimodal, or the density has a heavy right-hand tail, or the
distribution has an increasing hazard rate.
This talk consists of an exposition of these families with an emphasis on their characteristics
This talk is based on joint work with Albert Marshall which culminated in the book Life Distributions